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Stability and Control of Large-Scale Dynamical Systems by Sergey G. Nersesov, Wassim M. Haddad

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Chapter Twelve

Finite-Time Stabilization of Large-Scale Impulsive Dynamical Systems

12.1 Introduction

As noted in Chapter 6, finite-time stability implies Lyapunov stability and convergence of system trajectories to an equilibrium state in finite time, and hence, is a stronger notion than asymptotic stability. For continuous-time dynamical systems, finite-time stability implies non-Lipschitzian dynamics [24, 86] giving rise to non-uniqueness of solutions in reverse time. Uniqueness of solutions in forward time, however, can be preserved in the case of finite-time convergence. Sufficient conditions that ensure uniqueness of solutions in forward time in the absence of Lipschitz continuity are given in [1, 58, 108, 176]. Finite-time convergence ...

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