Switching Control For Unstable Subsysems

Switched systems that can be viewed as an important categoryof hybridsystems,are frequentlyusedformodeling manycomplexprocessesinnature and some practicalengineeringproblems. Different from the traditional general systems, switched system comprises of two components—a family ofsystems and a switching signal. This maybe lead system, especially the subsystems are possibly all unstable, to display very complicated dynamic characteristics.Therefore, it will be very meaningful and challenging tocarry out the studies on control of switched systems with possibly all unstable subsystems.Upto now, almostall results for stability of switched systemsrequirethe existence of(at least one) stable subsystem to ensure thestability of the whole switched system.The basic idea of these works is to activate thestable subsystem for sufficiently large time to compensate the state divergence caused by unstablesubsystems. However, when a switched system is composed of subsystems that may be all unstable, this promising idea clearly is notfeasible.This dissertation is concerned with the control problemfor a class of switched nonlinear systems possibly composedall unstable modes by using time-controlled switching signals and state-controlled switching signals, respectively. In chapters 2 and 3, based on the new proposed switching signals(average dwell time(ADT) and mode-dependent average dwell time(MDADT) switching signals),two sufficient conditions of stabilization for switched nonlinear systems withunstable subsystems are derived. Then, the T–S fuzzy modeling approachis applied to represent the underlying nonlinear system to make theobtained condition easily verified. Two novel multiple quadratic Lyapunovfunction approachesare also proposed, by which some conditions are provided in terms of a set of linear matrix inequalities to guarantee thederived T–S fuzzy system to be asymptotically stable.In chapter 4, the problem of adaptive control for a class of continuoustime switched linear systems is studied using a state-dependent switchingmethod.