Stability Analysis And Control Method For Switched Descriptor Systems

As an important class of special hybrid systems, switched descriptor systems, whichcomprise a collection of continuous-time or discrete-time descriptor subsystems together witha switching rule that specifies the switching among the subsystems to achieve the controlobjectives, can be used to describe a wide range of engineering systems. Compared with thenormal switched systems, the structure of switched descriptor systems is very complicatedbecause of the existences of a large number of practical problems, such as regularity,eliminating the pulse mode, state jump and the compatibility of initial state and so on.Moreover, in many actual systems, there exist random perturbation, time-delay, uncertainty,nonlinear disturbance and other factors, so it is inevitably difficult to analyze and design thecontroller, and a lot of control theory research and practical problems in engineeringapplication need to be dealt with for switched descriptor systems.Based on the common Lyapunov function method combined with the convex combinationtechnique, multiple Lyapunov function method and the average dwell time method, thecontrol issues of robust H?memory state feedback control, robust H?guaranteed costcontrol?input-to-state stability?uniform finite time stability and finite time boundness arediscussed respectively. This paper is divided into six chapters, and the main study contents areas follow:1) The problems of robust H?control and memory state feedback stabilization forcontinuous-time and discrete-time uncertain switched descriptor systems with delays arediscussed respectively. First, suppose that the uncertain parameters are norm bounded, and theidea of memory state feedback control is introduced for a class of uncertain time-varyingdelayed switched descriptor systems with nonlinear disturbance. Sufficient conditions for theexistences of robust H?memory state feedback controller in terms of linear matrixinequalities (LMIS) and switching rules are presented based on the common Lyapunovfunction and linear matrix inequality approach, and the designed controllers ensure that theclosed-loop systems satisfy the index with a presented H?disturbance attenuation level ?.Then, the results are generalized to study a class of discrete-time uncertain switcheddescriptor systems with delays.2) First, the concepts of robust H?guaranteed cost control is proposed. Then, theproblems for uncertain switched descriptor systems with constant time delays andtime-varying delays are addressed respectively. The delay-dependent sufficient conditions androbust H?guaranteed cost control controller in terms of linear matrix inequalities arepresented. Based on the above research foundation, and the common Lyapunov functionmethod combined with the convex combination technique, designing the correspondingswitching rules, the problems of robust H?guaranteed cost control and memory statefeedback stabilization for uncertain switched descriptor systems with time-varying delay andnonlinear perturbation are discussed. 3) The problems of uniform finite-time stability, finite-time boundedness and statefeedback stabilization for continuous-time and discrete-time uncertain switched descriptorsystems are addressed based on the multiple Lyapunov funcntions?switched Lyapunovfuncntions approaches and average dwell time technique. First, the concepts of uniformfinite-time stability and finite-time boundedness are generalized to switched descriptorsystems. In addition, sufficient conditions for the existences of state feedback controllers interms of linear matrix inequalities are obtained with arbitrary switching rules, whichguarantee that the continuous-time and discrete-time uncertain switched descriptor systemsare uniform finite-time stable and finite-time bounded respectively. Compared with statetransition matrix method, to some extent, the proposed results reduce the difficulty ofcontroller designing in actual application.4) Based on the average dwell time approach and Gronwall-Bellman inequality approach,the control issue of input-to-state stability for a class of nonlinear time-delayed switcheddescriptor systems is divided into two cases to discuss. When each subsystem is input-to-statestable, or some subsystems are not input-to-state stable, according to the definition ofinput-to-state stable, suppose that the control inputs are bounded and design thecorresponding switching rules, the sufficient conditions are given dispense with constructingthe Lyapunov function and specific form of control input, which guarantee that the nonlineartime-delayed switched descriptor systems are input-to-state stable.