The Robust L₂-gain Control For A Class Of Cascaded Switched Nonlinear Systems

A switched system is a class of important hybrid systems that consist of a seriesof continuous-time or discrete-time subsystems and a switching rule whichdetermines the switching between the subsystems．The study of switched systems hasattracted a great interestion in recent years．Such an interest comes from the fact thatmany practical systems are inherently multimode and the idea of switching betweendifferent controllers is widely applied for intelligent control fields． Moreover,switched systems are much more complicated than non-switched systems．Sinceswitching between stable subsystems could cause instability, that is, the stability of allsubsystems is not enough to ensure the stability of the switched system underarbitrary switching, it is necessary to impose other proper additional conditions toensure the stability under arbitrary switching for the switched systems.In this dissertation, we study the robust finiteL₂-gain control for a class ofcascade switched nonlinear systems with parameter uncertainty．In this paper, eachsubsystem of the switched system is consisted of a zero-input asymptotically stablenonlinear part which is a lower dimension switched system, and of a linearizablepart．The control channel of each subsystem includes the uncertainty．We givesufficient conditions under which the nonlinear feedback controllers are derived toguarantee theL₂-gain of the closed-loop switched system is less than a prespecifiedvalue for all admissible uncertainty under arbitrary switching．Moreover, we alsodevelop theL₂-gain controllers for the switched systems with non-minimum phasecase.