Publications by Eduardo D. Sontag in year 2002
Articles in journal or book chapters
  1. M. Arcak, D. Angeli, and E.D. Sontag. A unifying integral ISS framework for stability of nonlinear cascades. SIAM J. Control Optim., 40(6):1888-1904, 2002. [PDF] [doi:] Keyword(s): input to state stability, integral input to state stability, iISS, ISS.
    We analyze nonlinear cascades in which the driven subsystem is integral ISS, and characterize the admissible integral ISS gains for stability. This characterization makes use of the convergence speed of the driving subsystem, and allows a larger class of gain functions when the convergence is faster. We show that our integral ISS gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem.

  2. M. Chaves and E.D. Sontag. State-Estimators for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type. European J. Control, 8:343-359, 2002. [PDF] Keyword(s): observability, zero-deficiency networks, systems biology, biochemical networks, observers, nonlinear stability, dynamical systems.
    This paper provides a necessary and sufficient condition for detectability, and an explicit construction of observers when this condition is satisfied, for chemical reaction networks of the Feinberg-Horn-Jackson zero deficiency type.

  3. B.N. Kholodenko, A. Kiyatkin, F.J. Bruggeman, E.D. Sontag, H.V. Westerhoff, and J. Hoek. Untangling the wires: a novel strategy to trace functional interactions in signaling and gene networks. Proceedings of the National Academy of Sciences USA, 99:12841-12846, 2002. [PDF] Keyword(s): modular response analysis, MAPK cascades, systems biology, biochemical networks, reverse engineering, gene and protein networks, protein networks, gene networks, systems identification.
    Emerging technologies have enabled the acquisition of large genomics and proteomics data sets. This paper proposes a novel quantitative method for determining functional interactions in cellular signaling and gene networks. It can be used to explore cell systems at a mechanistic level, or applied within a modular framework, which dramatically decreases the number of variables to be assayed. The topology and strength of network connections are retrieved from experimentally measured network responses to successive perturbations of all modules. In addition, the method can reveal functional interactions even when the components of the system are not all known, in which case some connections retrieved by the analysis will not be direct but correspond to the interaction routes through unidentified elements. The method is tested and illustrated using computer-generated responses of a modeled MAPK cascade and gene network.

  4. M. Krichman and E.D. Sontag. Characterizations of detectability notions in terms of discontinuous dissipation functions. Internat. J. Control, 75(12):882-900, 2002. [PDF] Keyword(s): input to state stability, detectability, input to output stability, detectability.
    We consider a new Lyapunov-type characterization of detectability for nonlinear systems without controls, in terms of lower-semicontinuous (not necessarily smooth, or even continuous) dissipation functions, and prove its equivalence to the GASMO (global asymptotic stability modulo outputs) and UOSS (uniform output-to-state stability) properties studied in previous work. The result is then extended to provide a construction of a discontinuous dissipation function characterization of the IOSS (input-to-state stability) property for systems with controls. This paper complements a recent result on smooth Lyapunov characterizations of IOSS. The utility of non-smooth Lyapunov characterizations is illustrated by application to a well-known transistor network example.

  5. D. Liberzon, A. S. Morse, and E.D. Sontag. Output-input stability and minimum-phase nonlinear systems. IEEE Trans. Automat. Control, 47(3):422-436, 2002. [PDF] Keyword(s): input to state stability, detectability, minimum-phase systems, ISS, nonlinear control, minimum phase, adaptive control.
    This paper introduces and studies a new definition of the minimum-phase property for general smooth nonlinear control systems. The definition does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics. In the spirit of the ``input-to-state stability'' philosophy, it requires the state and the input of the system to be bounded by a suitable function of the output and derivatives of the output, modulo a decaying term depending on initial conditions. The class of minimum-phase systems thus defined includes all affine systems in global normal form whose internal dynamics are input-to-state stable and also all left-invertible linear systems whose transmission zeros have negative real parts. As an application, we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control.

  6. 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: [PDF] Keyword(s): input to state stability, integral input to state stability, ISS, iISS, nonlinear control, feedback stabilization.
    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.

  7. E.D. Sontag. Asymptotic amplitudes and Cauchy gains: A small-gain principle and an application to inhibitory biological feedback. Systems Control Lett., 47(2):167-179, 2002. [PDF] Keyword(s): MAPK cascades, cyclic feedback systems, small-gain.
    The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly feedback-dependent, steady states. A Lyapunov-like characterization allows the computation of gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops. An application in biology (MAPK signaling) is worked out in detail.

  8. E.D. Sontag. Correction to: ``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 (2001), no. 7, 1028--1047; MR1842137 (2002e:92006)]. IEEE Trans. Automat. Control, 47(4):705, 2002. [PDF] Keyword(s): zero-deficiency networks, systems biology, biochemical networks, nonlinear stability, dynamical systems.
    errata for Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction

  9. E.D. Sontag. For differential equations with r parameters, 2r+1 experiments are enough for identification. J. Nonlinear Sci., 12(6):553-583, 2002. [PDF] Keyword(s): identifiability, observability, systems biology, biochemical networks, parameter identification, real-analytic functions.
    Given a set of differential equations whose description involves unknown parameters, such as reaction constants in chemical kinetics, and supposing that one may at any time measure the values of some of the variables and possibly apply external inputs to help excite the system, how many experiments are sufficient in order to obtain all the information that is potentially available about the parameters? This paper shows that the best possible answer (assuming exact measurements and real analiticity) is 2r+1 experiments, where r is the number of parameters.

  10. E.D. Sontag and B.P. Ingalls. A small-gain theorem with applications to input/output systems, incremental stability, detectability, and interconnections. J. Franklin Inst., 339(2):211-229, 2002. [PDF] Keyword(s): input to state stability, ISS, Small-Gain Theorem, small gain.
    A general ISS-type small-gain result is presented. It specializes to a small-gain theorem for ISS operators, and it also recovers the classical statement for ISS systems in state-space form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems.

Conference articles
  1. D. Angeli and E.D. Sontag. A remark on monotone control systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 1876-1881, 2002.

  2. J.P. Hespanha, D. Liberzon, and E.D. Sontag. Nonlinear observability and an invariance principle for switched systems. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 4300-4305, 2002. [PDF] Keyword(s): observability.

  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]
    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.
    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. E.D. Sontag. Asymptotic amplitudes, Cauchy gains, an associated small-gain principle, and an application to inhibitory biological feedback. In Proc. IEEE Conf. Decision and Control, Las Vegas, Dec. 2002, IEEE Publications, pages 4318-4323, 2002. Keyword(s): cyclic feedback systems, small-gain.



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