1. A. C. Antoulas, E. D. Sontag, and Y. Yamamoto. Controllability and Observability, pages 264-281. John Wiley & Sons, Inc., 2001. [WWW] [PDF] [doi:10.1002/047134608X.W1006] Keyword(s): reachability, controllability, observability, Lie algebra accessibility.



2. E.D. Sontag. The ISS philosophy as a unifying framework for stability-like behavior. In Nonlinear control in the year 2000, Vol. 2 (Paris), volume 259 of Lecture Notes in Control and Inform. Sci., pages 443-467. Springer, London, 2001. [PDF] Keyword(s): input to state stability, integral input to state stability, iISS, ISS, input to output stability. Abstract:

   (This is an expository paper prepared for a plenary talk given at the Second Nonlinear Control Network Workshop, Paris, June 9, 2000.) The input to state stability (ISS) paradigm is motivated as a generalization of classical linear systems concepts under coordinate changes. A summary is provided of the main theoretical results concerning ISS and related notions of input/output stability and detectability. A bibliography is also included, listing extensions, applications, and other current work.




3. B. DasGupta and E.D. Sontag. A polynomial-time algorithm for checking equivalence under certain semiring congruences motivated by the state-space isomorphism problem for hybrid systems. Theor. Comput. Sci., 262(1-2):161-189, 2001. [PDF] [doi:http://dx.doi.org/10.1016/S0304-3975(00)00188-2] Keyword(s): hybrid systems, computational complexity. Abstract:

   The area of hybrid systems concerns issues of modeling, computation, and control for systems which combine discrete and continuous components. The subclass of piecewise linear (PL) systems provides one systematic approach to discrete-time hybrid systems, naturally blending switching mechanisms with classical linear components. PL systems model arbitrary interconnections of finite automata and linear systems. Tools from automata theory, logic, and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a "PL algebra" formalism. PL systems are of interest as controllers as well as identification models. Basic questions for any class of systems are those of equivalence, and, in particular, if state spaces are equivalent under a change of variables. This paper studies this state-space equivalence problem for PL systems. The problem was known to be decidable, but its computational complexity was potentially exponential; here it is shown to be solvable in polynomial-time.




4. W. Desch, H. Logemann, E. P. Ryan, and E.D. Sontag. Meagre functions and asymptotic behaviour of dynamical systems. Nonlinear Anal., 44(8, Ser. A: Theory Methods):1087-1109, 2001. [PDF] [doi:http://dx.doi.org/10.1016/S0362-546X(99)00323-5] Keyword(s): invariance principle. Abstract:

   A measurable function x from a subset J of R into a metric space X is said to be C-meagre if C is non-empty subset of X and, for every closed subset K of X disjoint from C, the preimage of K under x has finite Lebesgue measure. This concept of meagreness, applied to trajectories, is shown to provide a unifying framework which facilitates a variety of characterizations, extensions or generalizations of diverse facts pertaining to asymptotic behaviour of dynamical systems.




5. 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.




6. E.D. Sontag. Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction. IEEE Trans. Automat. Control, 46(7):1028-1047, 2001. [PDF] Keyword(s): zero-deficiency networks, systems biology, reaction networks, nonlinear stability, dynamical systems, kinetic proofreading, T cells, immunology. Abstract:

   This paper deals with the theory of structure, stability, robustness, and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks. The results given here extend, but are also heavily based upon, certain previous work by Feinberg, Horn, and Jackson, of which a self-contained and streamlined exposition is included. The theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by McKeithan for T-cell receptor signal transduction.

1. 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, ISS.



2. M. Arcak, D. Angeli, and E.D. Sontag. Stabilization of cascades using integral input-to-state stability. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001, IEEE Publications, 2001, pages 3814-3819, 2001. Keyword(s): nonlinear control, feedback stabilization, input to state stability.



3. M. Chaves and E.D. Sontag. An alternative observer for zero deficiency chemical networks. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 575-578, 2001. Keyword(s): observability, observers, zero-deficiency networks, systems biology, reaction networks, nonlinear stability, dynamical systems.



4. M. Chaves and E.D. Sontag. Observers for certain chemical reaction networks. In Proc. 2001 European Control Conf., Sep. 2001, pages 3715-3720, 2001. Keyword(s): zero-deficiency networks, systems biology, reaction networks, nonlinear stability, dynamical systems, observability, observers.



5. M. Chyba, N.E. Leonard, and E.D. Sontag. Optimality for underwater vehicles. In Proc. IEEE Conf. Decision and Control, Orlando, Dec. 2001,IEEE Publications, 2001, pages 4204-4209, 2001. [PDF] Keyword(s): optimal control.



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. P. Kuusela, D. Ocone, and E.D. Sontag. Remarks on the sample complexity for linear control systems identification. In IFAC Workshop on Adaptation and Learning in Control and Signal Processing, ALCOSP2001, Cernobbio-Como, Italy, 29-31 August, 2001, pages 431-436, 2001.



8. D. Liberzon, A.S. Morse, and E.D. Sontag. Output-input stability: a new variant of the minimum-phase property for nonlinear systems. In Proc. Nonlinear Control System Design Symposium, St. Petersburg, July 2001, pages 743-748, 2001. Keyword(s): input to state stability.



9. 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, ISS.

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