Stability Analysis And Control Of Switched Systems Based On Average Dwell Time Method

As one kind of hybrid systems,switched systems have been applied more and more widely,because of which the researchers are increasingly interested in the study of switched systems.Switched systems consist of different subsystems and a switching law that can decide how the subsystems switch.Because of the existence of switching law,the performance of switched systems has a relationship not only with each subsystem but also with the switching law closely.For instance,the stability of switched systems,one fundamental performance of a system,is closely related to switching law.Up to now,it is still a hot topic to study the stability of switched systems.In this paper,the stability of switched systems is investigated via mode-dependent average dwell time method.In the first chapter,the method of studying the stability of discrete-time switched systems is generalized to the study of aperiodic sampling systems.Besides,we obtain the stability condition of aperiodic sampling systems.Next,if the sampling interval is large and the package loss occurs,the corresponding state feedback controllers may lose efficacy.Thus,we continue investigating the stability condition of aperiodic sampling systems with unstable subsystems.Next,we study the stability of switched asynchronous positive systems both with stable and unstable subsystems.The state feedback controllers lag behind the subsystems for a period of time,which causes the phenomenon of asynchronous switching.Additionally,positive systems are one class of systems whose system states are non-negative all the time.At present,most of the researchers suppose that all the subsystems can be stabilized while solving the stability problem of switched asynchronous systems.But it is a very harsh condition.Therefore,we suppose that some of the subsystems from switched asynchronous positive systems cannot be stabilized.Via the method of limiting the running time of unstable subsystems,we obtain the stability condition of switched asynchronous positive systems.Then,we investigate the stabilization problem of switched asynchronous systems with constrained input.The constrained input derives from the saturation effect of the state feedback controllers that we have designed.Therefore,the output of the state feedback controller is saturation nonlinear.Considering this,we firstly obtain the stability condition of switched asynchronous systems with constrained input by choosing appropriate initial states and appropriate switching law.Additionally,some subsystems may not be stabilized by saturated state feedback controllers.Considering this,we study the stabilization problem of switched asynchronous systems with constrained input and unstable subsystems jointly.Finally,we study the stabilization problem of switched asynchronous positive systems with constrained input in discrete-time case.Different from the previous section,we restrict the initial states to one domain of attraction via using the technology of convex hull.After choosing an appropriate switching law,we can solve the saturation effect of actuator.Simultaneously,by solving the optimal problems,we can maximize the domain of attraction.Then,we investigate the boundedness of the system under external disturbance.After solving the optimal problem,we can get the biggest tolerant disturbance of the system.Besides,we study the ₁l-gain performance of the system.Moreover,we study the case when the solution to the nonlinear constrained optimization does not exist.