On Finite-time Stability For Nonlinear Switched Systems

Switched system is a crucial class of hybrid dynamical systems, which consists ofa family of subsystems described by diferential or diference equations and a switchingsignal governing the switching among them. Switched system can be used to mod-el many phenomena such as trafc control, chemical processing, network control andmulti-agent consensus and so on. For practical system, nonlinear perturbations and im-pulse efects are inevitable, which degrade the system performance or even destabilizethe system. This thesis concerns with the finite-time stability of nonlinear switchedimpulse system and the switched singular system. The main contents of this thesis areshown below.First, we deal with the finite-time stability problem of perturbed continuous-timeswitched system with impulse efects. The average dwell time approach, combiningwith the algebraic matrix theory, is utilized to derive a criterion guaranteeing the statetrajectory does not exceed a certain threshold over a pre-specified finite-time interval.The requirement that at least one subsystem should be stable to ensure asymptotic sta-bility is no longer needed.Second, for discrete case, we also consider the efect of nonlinear perturbation andimpulse efects. A sufcient condition is established, which guarantees that the system’sstate trajectory remains in a bounded region of the state space over a pre-specified finitetime interval if we impose a bound on the initial condition.Finally, we consider the issue of finite time stabilization of switched singular sys-tem in the presence of state jumps. Based on the state decomposition and pole as-signment technique, we give the equivalent definition of finite time stability of linearsingular system, which reveals the essence of finite time stability of switched singularsystem under the dynamical decomposition. Accordingly, the problem of the finite timestabilization of switched singular system with state jumps is discussed.