Showing papers by "Anthony N. Michel published in 2000"

Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach

Abstract: We study the stability properties of linear switched systems consisting of both Hurwitz stable and unstable subsystems using an average dwell time approach. We show that if the average dwell time is chosen sufficiently large and the total activation time of unstable subsystems is relatively small compared with that of Hurwitz stable subsystems, then exponential stability of a desired degree is guaranteed. We also derive a piecewise Lyapunov function for the switched system subjected to the switching law and the average dwell time scheme under consideration, and we extend these results to the case for which nonlinear norm-bounded perturbations exist in the subsystems. We show that when the norms of the perturbations are small, we can modify the switching law appropriately to guarantee that the solutions of the switched system converge to the origin exponentially with large average dwell time.

Hybrid output feedback stabilization of two-dimensional linear control systems

Abstract: We solve for two-dimensional SISO linear control systems the open problem whether there exists finite-state hybrid output feedback to stabilize the systems. We show that under reasonable assumptions, such as stabilizability and detectability conditions, the answer to this question is affirmative for the case of 2-state output feedback. We also address a simulation procedure to locate the stabilizable regions for switched systems consisting of two subsystems. We demonstrate the applicability of our results by considering several specific examples.

Robustness analysis of digital feedback control systems with time-varying sampling periods

Abstract: In the present paper, we study robustness properties of a class of digital feedback control systems with time-varying sampling periods consisting of an interconnection of a continuous-time nonlinear plant (described by systems of first-order ordinary differential equations), a nonlinear digital controller (described by systems of first-order ordinary difference equations), and appropriate interface elements between the plant and controller (A/D and D/A converters). For such systems, we establish results for exponential stability of an equilibrium (in the Lyapunov sense) in the presence of vanishing perturbations and for the boundedness of solutions (i.e., Lagrange stability) under the influence of nonvanishing perturbations. We apply these results in the study of quantization effects.

Moment stability of discontinuous stochastic dynamical systems

Abstract: In the present paper, we establish new Lyapunov and Lagrange stability results in the pth mean for a class of discontinuous stochastic dynamical systems. We apply these results in the qualitative analysis of a class of digital feedback control systems that are subjected to multiplicative and additive disturbances in the plants. The present results constitute natural extensions of our earlier results for discontinuous deterministic dynamical systems.

Common quadratic Lyapunov-like function with associated switching regions for two unstable second-order LTI systems

Abstract: In the present paper we utilize Lyapunov-like functions in the qualitative analysis of switched systems. Specifically for a class of second-order switched systems consisting of two unstable subsystems, explore in detail some necessary and sufficient conditions for the existence of common quadratic Lyapunov-like functions. We find that the existence of quadratic Lyapunov-like functions is closely related to conic switching laws.

Stability analysis of discontinuous dynamical systems using vector Lyapunov functions

Abstract: In this paper, we establish several stability results for discontinuous dynamical systems defined onR+=[0, ∞) which make use of vector Lyapunov functions. For the scalar case, these results yield in particular theprincipal Lyapunov stability results for discontinuous dynamical systems reported earlier. We demonstrate the applicability of our results by studying a class of interconnected discontinuous dynamical systems and several specific examples.