Electrical and Electronic Engineering - Research Publications
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ItemA note on input-to-state stability of sampled-data nonlinear systems(IEEE, 1998)It is shown for nonlinear systems that sampling sufficiently fast an input-to-state stabilizing (ISS) continuous time control law results in an ISS sampled-data control law. Two main features of our approach are: we show how the nonlinear sampled-data system can be modeled by a functional differential equation (FDE); we exploit a Razumikhin type theorem for ISS of FDE that was recently proved in [14] to analyze the sampled-data system.
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ItemOutput stabilization of nonlinear systems: Linear systems with positive outputs as a case study(IEEE, 1998)The problem of stabilization of linear systems for which only the magnitudes of outputs are measured is studied. A stabilizing controller is constructed which is input to state stability (ISS)-robust with respect to observation noise. Modal analysis and theorems are presented to prove the stabilization properties of the controller.
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ItemChanging supply functions in ISS systems: The discrete time case(IEEE - Institute of Electrical and Electronic Engineers, 2001)We characterize possible supply rates for input-to-state stable discrete-time systems and provide results that allow some freedom in modifying the supply rates. In particular, we show that the results derived by Sontag and Teel (1995) for continuous-time systems are achievable for discrete-time systems.
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ItemInput-to-state stability for nonlinear time-varying systems via averaging(SPRINGER LONDON LTD, 2001)We introduce two definitions of an averaged system for a time-varying ordinary differential equation with exogenous disturbances ("strong average" and "weak average"). The class of systems for which the strong average exists is shown to be strictly smaller than the class of systems for which the weak average exists. It is shown that input-to-state stability (ISS) of the strong average of a system implies uniform semi-global practical ISS of the actual system. This result generalizes the result of [TPA] which states that global asymptotic stability of the averaged system implies uniform semi-global practical stability of the actual system. On the other hand, we illustrate by an example that ISS of the weak average of a system does not necessarily imply uniform semi-global practical ISS of the actual system. However, ISS of the weak average of a system does imply a weaker semi-global practical "ISS-like" property for the actual system when the disturbances w are absolutely continuous and w, ẇ ∈ L∞. ISS of the weak average of a system is shown to be useful in a stability analysis of time-varying cascaded systems.
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ItemChanging supply functions in input to state stable systems: The discrete-time case(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2001-06)Supply rates for input-to-state stable (ISS) discrete-time systems is characterized and results are presented to modify the supply rates. It is shown that the results reported for continuous-time systems are achievable for discrete time systems. Determination of a Lyapunov function for a composite system is important.
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ItemPower characterizations of input-to-state stability and integral input-to-state stability(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2001-08)New notions of external stability for nonlinear systems are introduced, making use of average powers as signal norms and comparison functions as in the input-to-state stability (ISS) framework. Several new characterizations of ISS and integral ISS are presented in terms of the new notions. An example is discussed to illustrate differences and similarities of the newly introduced properties.
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ItemA note on input-to-state stability and averaging of systems with inputs(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2001-11)Two different definitions of an average for time-varying systems with inputs and a small parameter that were recently introduction in the literature are considered: "strong" and "weak" averages. It is shown that if the strong average is input-to-state stable (ISS), then the solutions of the actual system satisfy an integral bound in a semiglobal practical sense. The integral bound that we prove can be viewed as a generalization of the notion of finite-gain L2 stability, that was recently introduced in the literature. A similar result is proved for weak averages but the class of inputs for which the integral bound holds is smaller (Lipschitz inputs) than in the case of strong averages (measurable inputs).
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ItemAveraging with disturbances and closeness of solutions(ELSEVIER SCIENCE BV, 2000-08-15)We establish that, under appropriate conditions, the solutions of a time-varying system with disturbances converge uniformly on compact time intervals to the solutions of the system's average as the rate of change of time increases to infinity. The notions of "average" used for systems with disturbances are the "strong" and "weak" averages introduced in Nesic and Teel (D. Nešić, A.R. Teel, Input-to-state stability for time-varying nonlinear systems via averaging, 1999, submitted for publication. See also: On averaging and the ISS property, Proceedings of the 38th Conference on Decision and Control, Phoenix, AZ, December 1999, pp. 3346-3351.)
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ItemOutput feedback stabilization of a class of Wiener systems(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2000-09)A globally stabilizing output feedback controller is designed for a class of continuous-time Wiener systems. The Wiener systems we consider consist of a linear dynamical block and an output polynomial nonlinearity connected in series. The (hybrid) controller consists of three modes of operation which are periodically applied to the system. The controller achieves a dead-beat response of the closed-loop system.
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ItemSufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations(ELSEVIER, 1999-12-10)Given a parameterized (by sampling period T) family of approximate discrete-time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all T sufficiently small, we present conditions which guarantee that the same family of controllers semi-globally practically stabilizes the exact discrete-time model of the plant for sufficiently small sampling periods. When the family of controllers is locally bounded, uniformly in the sampling period, the inter-sample behavior can also be uniformly bounded so that the (time-varying) sampled-data model of the plant is uniformly semi-globally practically stabilized. The result justifies controller design for sampled-data nonlinear systems based on the approximate discrete-time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied. Our analysis is applicable to a wide range of time-discretization schemes and general plant models.