H_∞Control, Guaranteed Cost Control And Output Regulation Problem For Switched Systems With Multiple State-delays

Switched systems with time-delays are a very important class of hybrid systems, whichlinks closely with many engineering and theoretical problems. The behavior of hybridsystems is complicated due to the interactions of continuous dynamics and discrete dynamics.In addition, the appearances of delays increase the difficulty of system analysis and controlsynthesis. Researchers have got some satisfactory results about the switched delays systems,but for the switched systems with multiple delays the research is still very limited.This dissertation deals with the weighted H∞control problem, weighted guaranteed costcontrol problem and output regulation problem for some classes of switched systems withmultiple state-delays. The combination of free weighting matrix method and Jensen’s integralinequality avoids introducing too many slack matrices. The conservatism of the fixedweighting matrix method is reduced efficiently. The main contributions of this dissertation areas follows.The second chapter focuses on the weighted H∞control problem for a class of switchedsystems with multiple state-delays. Delay-dependent sufficient conditions for exponentialstabilization and weighted H∞control performance are developed respectively for hybrid stateand output feedback controllers under switching rules with average dwell time via linearmatrix inequalities. The combination of free weighting matrix method and Jensen’s integralinequality avoids introducing too many slack matrices. The computational complexity of thefree weighting matrix method is reduced efficiently. Two examples are presented to illustratethe feasibility of our results.In the third chapter, we discuss the weighted guaranteed cost control problem a class ofnonlinear cascade switched multiple state-delays systems. Based on the combination of thefree weighting matrix method and Jensen’s integral inequality, hybrid state feedbackcontrollers and switching rules satisfying the average dwell time are designed to ensuresufficient conditions of the weighted guaranteed cost control problem for the closed-loopsystems.In the fourth chapter, we investigate the output regulation problem for a class ofswitched systems with multiple state-delays. Combining the center manifold theory andinternal model principle gives the regulator equations with delays. Full information statefeedback controllers, error feedback controllers and the corresponding switching rules with average dwell time conditions are designed respectively to guarantee the solvability of theoutput regulation problem for the closed-loop systems.