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Publications of Eduardo D. Sontag jointly with Y. Wang
Articles in journal or book chapters
  1. E.D. Sontag, Y. Wang, and A. Megretski. Input classes for identification of bilinear systems. IEEE Transactions Autom. Control, 54:195-207, 2009. Note: Also arXiv math.OC/0610633, 20 Oct 2006, and short version in ACC'07.[PDF] Keyword(s): realization theory, observability, identifiability, bilinear systems.
    Abstract:
    This paper asks what classes of input signals are sufficient in order to completely identify the input/output behavior of generic bilinear systems. The main results are that step inputs are not sufficient, nor are single pulses, but the family of all pulses (of a fixed amplitude but varying widths) do suffice for identification.


  2. E.D. Sontag and Y. Wang. Uniformly Universal Inputs. In Alessandro Astolfi, editor, Analysis and Design of Nonlinear Control Systems, volume 224, pages 9-24. Springer-Verlag, London, 2007. [PDF] Keyword(s): observability, identification.
    Abstract:
    A result is presented showing the existence of inputs universal for observability, uniformly with respect to the class of all continuous-time analytic systems. This represents an ultimate generalization of a 1977 theorem, for bilinear systems, due to Alberto Isidori and Osvaldo Grasselli.


  3. E.D. Sontag and Y. Wang. A cooperative system which does not satisfy the limit set dichotomy. J. of Differential Equations, 224:373-384, 2006. [PDF] Keyword(s): dynamical systems, monotone systems.
    Abstract:
    The fundamental property of strongly monotone systems, and strongly cooperative systems in particular, is the limit set dichotomy due to Hirsch: if x < y, then either Omega(x) < Omega (y), or Omega(x) = Omega(y) and both sets consist of equilibria. We provide here a counterexample showing that this property need not hold for (non-strongly) cooperative systems.


  4. J. L. Mancilla-Aguilar, R. Garcža, E.D. Sontag, and Y. Wang. On the representation of switched systems with inputs by perturbed control systems. Nonlinear Anal., 60(6):1111-1150, 2005. [PDF]
    Abstract:
    This paper provides representations of switched systems described by controlled differential inclusions, in terms of perturbed control systems. The control systems have dynamics given by differential equations, and their inputs consist of the original controls together with disturbances that evolve in compact sets; their sets of maximal trajectories contain, as a dense subset, the set of maximal trajectories of the original system. Several applications to control theory, dealing with properties of stability with respect to inputs and of detectability, are derived as a consequence of the representation theorem.


  5. J. L. Mancilla-Aguilar, R. Garcža, E.D. Sontag, and Y. Wang. Uniform stability properties of switched systems with switchings governed by digraphs. Nonlinear Anal., 63(3):472-490, 2005. [PDF]
    Abstract:
    This paper develops characterizations of various uniform stability properties of switched systems described by differential inclusions, and whose switchings are governed by a digraph. These characterizations are given in terms of stability properties of the system with restricted switchings and also in terms of Lyapunov functions.


  6. D. Angeli, B.P. Ingalls, E.D. Sontag, and Y. Wang. Separation principles for input-output and integral-input-to-state stability. SIAM J. Control Optim., 43(1):256-276, 2004. [PDF] [doi:http://dx.doi.org/10.1137/S0363012902419047] Keyword(s): input to state stability.
    Abstract:
    We present new characterizations of input-output-to-state stability. This is a notion of detectability formulated in the ISS framework. Equivalent properties are presented in terms of asymptotic estimates of the state trajectories based on the magnitudes of the external input and output signals. These results provide a set of "separation principles" for input-output-to-state stability , characterizations of the property in terms of weaker stability notions. When applied to the closely related notion of integral ISS, these characterizations yield analogous results.


  7. D. Angeli, B.P. Ingalls, E.D. Sontag, and Y. Wang. Uniform global asymptotic stability of differential inclusions. J. Dynam. Control Systems, 10(3):391-412, 2004. [PDF] [doi:http://dx.doi.org/10.1023/B:JODS.0000034437.54937.7f] Keyword(s): differential inclusions.
    Abstract:
    The stability of differential inclusions defined by locally Lipschitz compact valued maps is addressed. It is shown that if such a differential inclusion is globally asymptotically stable, then in fact it is uniformly globally asymptotically stable (with respect to initial states in compacts). This statement is trivial for differential equations, but here we provide the extension to compact (not necessarily convex) valued differential inclusions. The main result is presented in a context which is useful for control-theoretic applications: a differential inclusion with two outputs is considered, and the result applies to the property of global error detectability.


  8. D. Angeli, E.D. Sontag, and Y. Wang. Input-to-state stability with respect to inputs and their derivatives. Internat. J. Robust Nonlinear Control, 13(11):1035-1056, 2003. [PDF] Keyword(s): input to state stability, input to state stability.
    Abstract:
    A new notion of input-to-state stability involving infinity norms of input derivatives up to a finite order k is introduced and characterized. An example shows that this notion of stability is indeed weaker than the usual ISS. Applications to the study of global asymptotic stability of cascaded nonlinear systems are discussed.


  9. B.P. Ingalls, E.D. Sontag, and Y. Wang. An infinite-time relaxation theorem for differential inclusions. Proc. Amer. Math. Soc., 131(2):487-499, 2003. [PDF]
    Abstract:
    The fundamental relaxation result for Lipschitz differential inclusions is the Filippov-Wazewski Relaxation Theorem, which provides approximations of trajectories of a relaxed inclusion on finite intervals. A complementary result is presented, which provides approximations on infinite intervals, but does not guarantee that the approximation and the reference trajectory satisfy the same initial condition.


  10. D. Liberzon, E.D. Sontag, and Y. Wang. Universal construction of feedback laws achieving ISS and integral-ISS disturbance attenuation. Systems Control Lett., 46(2):111-127, 2002. Note: Errata here: http://www.math.rutgers.edu/(tilde)sontag/FTPDIR/iiss-clf-errata.pdf. [PDF] Keyword(s): input to state stability, nonlinear control, feedback stabilization.
    Abstract:
    We study nonlinear systems with both control and disturbance inputs. The main problem addressed in the paper is design of state feedback control laws that render the closed-loop system integral-input-to-state stable (iISS) with respect to the disturbances. We introduce an appropriate concept of control Lyapunov function (iISS-CLF), whose existence leads to an explicit construction of such a control law. The same method applies to the problem of input-to-state stabilization. Converse results and techniques for generating iISS-CLFs are also discussed.


  11. M. Krichman, E.D. Sontag, and Y. Wang. Input-output-to-state stability. SIAM J. Control Optim., 39(6):1874-1928, 2001. [PDF] [doi:http://dx.doi.org/10.1137/S0363012999365352] Keyword(s): input to state stability.
    Abstract:
    This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of "norm-estimators", and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.


  12. D. Angeli, E.D. Sontag, and Y. Wang. A characterization of integral input-to-state stability. IEEE Trans. Automat. Control, 45(6):1082-1097, 2000. [PDF] Keyword(s): input to state stability.
    Abstract:
    Just as input to state stability (ISS) generalizes the idea of finite gains with respect to supremum norms, the new notion of integral input to state stability (IISS) generalizes the concept of finite gain when using an integral norm on inputs. In this paper, we obtain a necessary and sufficient characterization of the IISS property, expressed in terms of dissipation inequalities.


  13. D. Angeli, E.D. Sontag, and Y. Wang. Further equivalences and semiglobal versions of integral input to state stability. Dynamics and Control, 10(2):127-149, 2000. [PDF] [doi:http://dx.doi.org/10.1023/A:1008356223747] Keyword(s): input to state stability.
    Abstract:
    This paper continues the study of the integral input-to-state stability (IISS) property. It is shown that the IISS property is equivalent to one which arises from the consideration of mixed norms on states and inputs, as well as to the superposition of a ``bounded energy bounded state'' requirement and the global asymptotic stability of the unforced system. A semiglobal version of IISS is shown to imply the global version, though a counterexample shows that the analogous fact fails for input to state stability (ISS). The results in this note complete the basic theoretical picture regarding IISS and ISS.


  14. E.D. Sontag and Y. Wang. Lyapunov characterizations of input to output stability. SIAM J. Control Optim., 39(1):226-249, 2000. [PDF] [doi:http://dx.doi.org/10.1137/S0363012999350213] Keyword(s): input to state stability.
    Abstract:
    This paper presents necessary and sufficient characterizations of several notions of input to output stability. Similar Lyapunov characterizations have been found to play a key role in the analysis of the input to state stability property, and the results given here extend their validity to the case when the output, but not necessarily the entire internal state, is being regulated.


  15. E.D. Sontag and Y. Wang. Notions of input to output stability. Systems Control Lett., 38(4-5):235-248, 1999. [PDF] Keyword(s): input to state stability.
    Abstract:
    This paper deals with several related notions of output stability with respect to inputs (which may be thought of as disturbances). The main such notion is called input to output stability (IOS), and it reduces to input to state stability (ISS) when the output equals the complete state. For systems with no inputs, IOS provides a generalization of the classical concept of partial stability. Several variants, which formalize in different manners the transient behavior, are introduced. The main results provide a comparison among these notions


  16. E.D. Sontag and Y. Wang. Output-to-state stability and detectability of nonlinear systems. Systems Control Lett., 29(5):279-290, 1997. [PDF] [doi:http://dx.doi.org/10.1016/S0167-6911(97)90013-X] Keyword(s): input to state stability, detectability, input to state stability.
    Abstract:
    The notion of input-to-state stability (ISS) has proved to be useful in nonlinear systems analysis. This paper discusses a dual notion, output-to-state stability (OSS). A characterization is provided in terms of a dissipation inequality involving storage (Lyapunov) functions. Combining ISS and OSS there results the notion of input/output-to-state stability (IOSS), which is also studied and related to the notion of detectability, the existence of observers, and output injection.


  17. Y. Lin, E.D. Sontag, and Y. Wang. A smooth converse Lyapunov theorem for robust stability. SIAM J. Control Optim., 34(1):124-160, 1996. [PDF] [doi:http://dx.doi.org/10.1137/S0363012993259981] Keyword(s): input to state stability.
    Abstract:
    This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of well-known classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded time-varying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets.


  18. E.D. Sontag and Y. Wang. New characterizations of input-to-state stability. IEEE Trans. Automat. Control, 41(9):1283-1294, 1996. [PDF] Keyword(s): input to state stability.
    Abstract:
    We present new characterizations of the Input to State Stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variations proposed in the literature.


  19. Y. Lin, E.D. Sontag, and Y. Wang. Input to state stabilizability for parametrized families of systems. Internat. J. Robust Nonlinear Control, 5(3):187-205, 1995. [PDF]
    Abstract:
    This paper studies various stability issues for parameterized families of systems, including problems of stabilization with respect to sets. The study of such families is motivated by robust control applications. A Lyapunov-theoretic necessary and sufficient characterization is obtained for a natural notion of robust uniform set stability; this characterization allows replacing ad hoc conditions found in the literature by more conceptual stability notions. We then use these techniques to establish a result linking state space stability to ``input to state'' (bounded-input bounded-state) stability. In addition, the preservation of stabilizability under certain types of cascade interconnections is analyzed.


  20. E.D. Sontag and Y. Wang. On characterizations of the input-to-state stability property. Systems Control Lett., 24(5):351-359, 1995. [PDF] [doi:http://dx.doi.org/10.1016/0167-6911(94)00050-6] Keyword(s): input to state stability.
    Abstract:
    We show that the well-known Lyapunov sufficient condition for input-to-state stability is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided.


  21. Y. Wang and E.D. Sontag. Orders of input/output differential equations and state-space dimensions. SIAM J. Control Optim., 33(4):1102-1126, 1995. [PDF] [doi:http://dx.doi.org/10.1137/S0363012993246828] Keyword(s): identifiability, observability, realization theory.
    Abstract:
    This paper deals with the orders of input/output equations satisfied by nonlinear systems. Such equations represent differential (or difference, in the discrete-time case) relations between high-order derivatives (or shifts, respectively) of input and output signals. It is shown that, under analyticity assumptions, there cannot exist equations of order less than the minimal dimension of any observable realization; this generalizes the known situation in the classical linear case. The results depend on new facts, themselves of considerable interest in control theory, regarding universal inputs for observability in the discrete case, and observation spaces in both the discrete and continuous cases. Included in the paper is also a new and simple self-contained proof of Sussmann's universal input theorem for continuous-time analytic systems.


  22. Y. Wang and E.D. Sontag. Algebraic differential equations and rational control systems. SIAM J. Control Optim., 30(5):1126-1149, 1992. [PDF] Keyword(s): identifiability, observability, realization theory, input/output system representations.
    Abstract:
    It is shown that realizability of an input/output operators by a finite-dimensional continuous-time rational control system is equivalent to the existence of a high-order algebraic differential equation satisfied by the corresponding input/output pairs ("behavior"). This generalizes, to nonlinear systems, the classical equivalence between autoregressive representations and finite dimensional linear realizability.


  23. Y. Wang and E.D. Sontag. Generating series and nonlinear systems: analytic aspects, local realizability, and i/o representations. Forum Math., 4(3):299-322, 1992. [PDF] Keyword(s): identifiability, observability, realization theory, input/output system representations.
    Abstract:
    This paper studies fundamental analytic properties of generating series for nonlinear control systems, and of the operators they define. It then applies the results obtained to the extension of facts, which relate realizability and algebraic input/output equations, to local realizability and analytic equations.


  24. E.D. Sontag and Y. Wang. Input/output equations and realizability. In Realization and modelling in system theory (Amsterdam, 1989), volume 3 of Progr. Systems Control Theory, pages 125-132. Birkhšuser Boston, Boston, MA, 1990. [PDF] Keyword(s): identifiability, observability, realization theory.


  25. E.D. Sontag and Y. Wang. Pole shifting for families of linear systems depending on at most three parameters. Linear Algebra Appl., 137/138:3-38, 1990. [PDF] Keyword(s): systems over rings, systems over rings.
    Abstract:
    We prove that for any family of n-dimensional controllable linear systems, continuously parameterized by up to three parameters, and for any continuous selection of n eigenvalues (in complex conjugate pairs), there is some dynamic controller of dimension 3n which is itself continuously parameterized and for which the closed-loop eigenvalues are these same eigenvalues, each counted 4 times. An analogous result holds also for smooth parameterizations.


  26. Y. Wang and E.D. Sontag. On two definitions of observation spaces. Systems Control Lett., 13(4):279-289, 1989. [PDF] [doi:http://dx.doi.org/10.1016/0167-6911(89)90116-3] Keyword(s): observability, identifiability, observability, realization theory.
    Abstract:
    This paper establishes the equality of the observation spaces defined by means of piecewise constant controls with those defined in terms of differentiable controls.


Conference articles
  1. E.D. Sontag, Y. Wang, and A. Megretski. Remarks on Input Classes for Identification of Bilinear Systems. In Proceedings American Control Conf., New York, July 2007, pages 4345-4350, 2007. Keyword(s): realization theory, observability, identifiability, bilinear systems.


  2. J.L. Mancilla-Aguilar, R. Garcža, E.D. Sontag, and Y. Wang. Representation of switched systems by perturbed control systems. In Proc. IEEE Conf. Decision and Control, Paradise Island, Bahamas, Dec. 2004, IEEE Publications, pages 3259-3264, 2004.


  3. B.P. Ingalls, E.D. Sontag, and Y. Wang. A relaxation theorem for differential inclusions with applications to stability properties. In D. Gilliam and J. Rosenthal, editors, Mathematical Theory of Networks and Systems, Electronic Proceedings of MTNS-2002 Symposium held at the University of Notre Dame, August 2002, 2002. Note: (12 pages). [PDF]
    Abstract:
    The fundamental Filippov--Wazwski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. In a recent paper of ours, a complementary result was provided for inclusions with finite dimensional state spaces which says that the approximation can be carried out over non-compact or infinite intervals provided one does not insist on the same initial values. This note extends the infinite-time relaxation theorem to the inclusions whose state spaces are Banach spaces. To illustrate the motivations for studying such approximation results, we briefly discuss a quick application of the result to output stability and uniform output stability properties.


  4. B.P. Ingalls, E.D. Sontag, and Y. Wang. Measurement to error stability: a notion of partial detectability for nonlinear systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 3946-3951, 2002. [PDF] Keyword(s): input to state stability.
    Abstract:
    For systems whose output is to be kept small (thought of as an error output), the notion of input to output stability (IOS) arises. Alternatively, when considering a system whose output is meant to provide information about the state (i.e. a measurement output), one arrives at the detectability notion of output to state stability (OSS). Combining these concepts, one may consider a system with two types of outputs, an error and a measurement. This leads naturally to a notion of partial detectability which we call measurement to error stability (MES). This property characterizes systems in which the error signal is detectable through the measurement signal. This paper provides a partial Lyapunov characterization of the MES property. A closely related property of stability in three measures (SIT) is introduced, which characterizes systems for which the error decays whenever it dominates the measurement. The SIT property is shown to imply MES, and the two are shown to be equivalent under an additional boundedness assumption. A nonsmooth Lyapunov characterization of the SIT property is provided, which yields the partial characterization of MES. The analysis is carried out on systems described by differential inclusions -- implicitly incorporating a disturbance input with compact value-set.


  5. D. Angeli, E.D. Sontag, and Y. Wang. A note on input-to-state stability with input derivatives. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 720-725, 2001. Keyword(s): input to state stability.


  6. B.P. Ingalls, D. Angeli, E.D. Sontag, and Y. Wang. Asymptotic characterizations of IOSS. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001, pages 881-886, 2001. Keyword(s): nonlinear control, feedback stabilization, input to state stability.


  7. E.D. Sontag, B.P. Ingalls, and Y. Wang. Generalizations of asymptotic gain characterizations of ISS to input-to-output stability. In Proc. American Control Conf., Arlington, June 2001, pages 2279-2284, 2001. Keyword(s): input to state stability.


  8. B.P. Ingalls, E.D. Sontag, and Y. Wang. Remarks on input to output stability. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 1226-1231, 1999. Keyword(s): input to state stability.


  9. Z-P. Jiang, E.D. Sontag, and Y. Wang. Input-to-state stability for discrete-time nonlinear systems. In Proc. 14th IFAC World Congress, Vol E (Beijing), pages 277-282, 1999. [PDF] Keyword(s): input to state stability, input to state stability, discrete-time.
    Abstract:
    This paper studies the input-to-state stability (ISS) property for discrete-time nonlinear systems. We show that many standard ISS results may be extended to the discrete-time case. More precisely, we provide a Lyapunov-like sufficient condition for ISS, and we show the equivalence between the ISS property and various other properties, as well as provide a small gain theorem.


  10. M. Krichman, E.D. Sontag, and Y. Wang. Lyapunov characterizations of input-ouput-to-state stability. In Proc. IEEE Conf. Decision and Control, Phoenix, Dec. 1999, IEEE Publications, 1999, pages 2070-2075, 1999. Keyword(s): input to state stability.


  11. D. Liberzon, E.D. Sontag, and Y. Wang. On integral-input-to-state stabilization. In Proc. American Control Conf., San Diego, June 1999, pages 1598-1602, 1999. [PDF] Keyword(s): input to state stability, control-Lyapunov functions.
    Abstract:
    This paper continues the investigation of the recently introduced integral version of input-to-state stability (iISS). We study the problem of designing control laws that achieve iISS disturbance attenuation. The main contribution is an appropriate concept of control Lyapunov function (iISS-CLF), whose existence leads to an explicit construction of such a control law. The results are compared and contrasted with the ones available for the ISS case.


  12. D. Angeli, E.D. Sontag, and Y. Wang. A remark on integral input to state stability. In Proc. IEEE Conf. Decision and Control, Tampa, Dec. 1998, IEEE Publications, 1998, pages 2491-2496, 1998. Keyword(s): input to state stability.


  13. E.D. Sontag and Y. Wang. A notion of input to output stability. In Proc. European Control Conf., Brussels, July 1997, 1997. Note: (Paper WE-E A2, CD-ROM file ECC958.pdf, 6 pages). [PDF] Keyword(s): input to state stability, input to state stability.
    Abstract:
    This paper deals with a notion of "input to output stability (IOS)", which formalizes the idea that outputs depend in an "aymptotically stable" manner on inputs, while internal signals remain bounded. When the output equals the complete state, one recovers the property of input to state stability (ISS). When there are no inputs, one has a generalization of the classical concept of partial stability. The main results provide Lyapunov-function characterizations of IOS.


  14. E.D. Sontag and Y. Wang. Detectability of nonlinear systems. In Proc. Conf. on Information Sciences and Systems (CISS 96), Princeton, NJ, pages 1031-1036, 1996. [PDF] Keyword(s): detectability, input to state stability.
    Abstract:
    Contains a proof of a technical step, which was omitted from the journal paper due to space constraints


  15. E.D. Sontag and Y. Wang. On characterizations of input-to-state stability with respect to compact sets. In Proceedings of IFAC Non-Linear Control Systems Design Symposium, (NOLCOS '95), Tahoe City, CA, June 1995, pages 226-231, 1995. [PDF] Keyword(s): input to state stability.
    Abstract:
    Previous characterizations of ISS-stability are shown to generalize without change to the case of stability with respect to sets. Some results on ISS-stabilizability are mentioned as well.


  16. E.D. Sontag and Y. Wang. Various results concerning set input-to-state stability. In Proc. IEEE Conf. Decision and Control, New Orleans, Dec. 1995, IEEE Publications, 1995, pages 1330-1335, 1995. Keyword(s): input to state stability.


  17. Y. Lin, E.D. Sontag, and Y. Wang. Recent results on Lyapunov-theoretic techniques for nonlinear stability. In Proc. Amer. Automatic Control Conf., Baltimore, June 1994, pages 1771-1775, 1994.


  18. E.D. Sontag and Y. Wang. Notions equivalent to input-to-state stability. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 3438-3443, 1994. Keyword(s): input to state stability.


  19. E.D. Sontag and Y. Wang. Orders of I/O equations and uniformly universal inputs. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 1994, IEEE Publications, 1994, pages 1270-1275, 1994. Keyword(s): identifiability, observability, realization theory.


  20. Y. Lin, E.D. Sontag, and Y. Wang. Lyapunov-function characterizations of stability and stabilization for parameterized families of systems. In Proc. IEEE Conf. Decision and Control, San Antonio, Dec. 1993, IEEE Publications, 1993, pages 1978-1983, 1993.


  21. E.D. Sontag and Y. Wang. I/O equations in discrete and continuous time. In Proc. IEEE Conf. Decision and Control, Tucson, Dec. 1992, IEEE Publications, 1992, pages 3661-3662, 1992. Keyword(s): identifiability, observability, realization theory.


  22. E.D. Sontag and Y. Wang. I/O equations for nonlinear systems and observation spaces. In Proc. IEEE Conf. Decision and Control, Brighton, UK, Dec. 1991, IEEE Publications, 1991, pages 720-725, 1991. [PDF] Keyword(s): identifiability, observability, realization theory.
    Abstract:
    This paper studies various types of input/output representations for nonlinear continuous time systems. The algebraic and analytic i/o equations studied in previous papers by the authors are generalized to integral and integro-differential equations, and an abstract notion is also considered. New results are given on generic observability, and these results are then applied to give conditions under which that the minimal order of an equation equals the minimal possible dimension of a realization, just as with linear systems but in contrast to the discrete time nonlinear theory.


  23. Y. Wang and E.D. Sontag. Realization of families of generating series: differential algebraic and state space equations. In Proc. 11th IFAC World Congress, Tallinn, former USSR, 1990, pages 62-66, 1990. Keyword(s): identifiability, observability, realization theory.


  24. Y. Wang and E.D. Sontag. A new result on the relation between differential-algebraic realizability and state space realizations. In Proc. Conf. Info. Sciences and Systems, Johns Hopkins University Press, 1989, pages 143-147, 1989. Keyword(s): identifiability, observability, realization theory.


  25. Y. Wang and E.D. Sontag. Realization and input/output relations: the analytic case. In Proceedings of the 28th IEEE Conference on Decision and Control, Vol. 1--3 (Tampa, FL, 1989), New York, pages 1975-1980, 1989. IEEE. Keyword(s): identifiability, observability, realization theory.



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