Research On Stabilization Of Restricted Switched Systems Based On MDADT Method

As an special class of hybrid systems,switched systems is an important model to study the hybrid system from the point of view of system control.Switched system is a dynamical system,which consists of a finite number ofsubsystems and a logical rule that orchestrates switching between these subsystems.Meanwhile,there exist safety consideration or inherentlimit of equipment,so we have to consider the states constraints.Therefore,many analysis and design problems deserve further investigation.Switched positive systems arise inmany engineering applications,such as network congestion controlsystems,infectious disease controlsystems.The main contributions of this paper are as follows.First of all,the paper introduces the concept of switched systems,switched positive systems and switched systems with state constraints.It includes the research background of the switched systems,the main research questionsand methods.Based on above discussion,this articleinvestigatesthe stabilization problem of switched systems with state constraintsin continuous-time and discrete-time contexts,respectively.Animprovedmode-dependentaverage dwell time method(MDADT)is presented toconsiders different decay rates of a Lyapunov function related to each of the activesubsystems corresponding to the saturations occur or not,respectively.Based on the MDADT method,the sufficientconditions and state feedback controllers for stabilization of the switched system arederived.It is shown thatthe improved average dwell time method is less conservative than the standardADT method.The paper deals with the stabilization problem of continuous-time switched positive systemswith state constraints based on mode-dependent average dwell time(MDADT)in the next.First of all,themodel of continuous-time switched positive system is given.Then,using the MDADT method proposed above,we give the sufficientconditions and state feedback controllers for stabilization of the continuoustime switched positive system.Finally,a numerical simulation example is given to illustrate the effectiveness of the MDADT method.Finally,the results of the thesis are summarized and the further research topics arepresented.