On Stabilizability Of Complex Switching System

As an important class of hybrid dynamical system, a switched system is composed ofseveral continuous-time subsystems or discrete-time subsystems and the switching signalsamong them. Due to the existence of the switching rules, switching system is fundamentallydifferent from traditional continuous-time systems or discrete-time systems, and its dynamicsmay become very complicated, for example, its stability may change, the state trajectory mayjump at the switching point. Hence, it is very important to choose the proper switching signal.Switched systems exist widely in engineering technology such as computer disk system,robotics, power systems, air traffic management, automated vehicles, etc. During the lastthree decades, there is an increasing interest on the analysis, modeling, synthesis, and controlof switched system. Nowadays, more and more people have paid attention to the analysis ofthe switched systems and the study of the switching control.This dissertation devotes on the study of asymptotic stablility of the discrete-time planarswitched system and discrete-time planar impulse switched system, exponential stabilizabilityof continuous-time switched system and switched system with interval time-varying delay.Firstly, we study the stabilization problem of discrete-time planar switched linearsystems. When all subsystems are controllable, based on an estimate on state transition matrix,we establish a sufficient condition such that the switched system is stabilizable under arbitraryswitching signal with given switching frequency. When there exists at least one uncontrollablesubsystem, a sufficient condition is also given to guarantee the stabilization of the switchedsystem under any switching signal with given switching frequency. We study the stabilizationproblem of discrete-time planar switched linear systems with nonlinear impulse. When allsubsystems are controllable, we establish a sufficient condition such that the switched systemis stabilizable under bounded impulse and arbitrary switching signal with given switchingfrequency. When there exists at least one uncontrollable subsystem, a sufficient condition isalso given to guarantee the stabilization of the switched system under bounded impulse andappropriate switching signal. The work in this section forwards the study in the switchedlinear systems.Secondly, we study the stabilization problem of switched systems with both controllableand uncontrollable subsystems. By using an average dwell time approach, we first establish asufficient condition such that the switched system is exponentially stabilizable underappropriate switching signals. We also extend this result to the switched system withnonlinear impulse effects and disturbances. Thirdly, we identify a class of switching sequences to guarantee exponential stability ofswitched systems with impulse effects and interval time-varying delays. By taking both thelower bound and upper bound of delay into consideration in the multiple Lyapunov functions,we establish several new stability criteria given in terms of linear matrix inequalities that canbe solved easily by using the Matlab’s LMI Toolbox.