Finite-time stabilization of nonlinear impulsive dynamical.pdfVIP

Nonlinear Analysis: Hybrid Systems 2 (2008) 832–845 /locate/nahs Finite-time stabilization of nonlinear impulsive dynamical systems Sergey G. Nersesova,∗, Wassim M. Haddadb,1 a Department of Mechanical Engineering, Villanova University, Villanova, PA 19085-1681, United States b School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0150, United States Received 11 June 2007; accepted 11 December 2007 Abstract Finite-time stability involves dynamical systems whose trajectories converge to a Lyapunov stable equilibrium state in finite time. For continuous-time dynamical systems finite-time convergence implies nonuniqueness of system solutions in reverse time, and hence, such systems possess non-Lipschitzian dynamics. For impulsive dynamical systems, however, it may be possible to reset the system states to an equilibrium state achieving finite-time convergence without requiring non-Lipschitzian system dynamics. In this paper, we develop sufficient conditions for finite-time stability of impulsive dynamical systems using both scalar and vector Lyapunov functions. Furthermore, we design hybrid finite-time stabilizing controllers for impulsive dynamical systems that are robust against full modelling uncertainty. Finally, we present a numerical example for finite-time stabilization of large-scale impulsive dynamical systems. c 2008 Elsevier Ltd. All rights reserved. Keywords: Finite-time stability; Finite-time convergence; Impulsive systems; Zeno solutions; Non-Lipschitzian dynamics; Finite-time stabilization; Control Lyapunov functions 1. Introduction The mathematical descriptions of many hybrid dynamical systems can be cha