The Stability And Stabilization Design Of Uncertain Hybrid Systems

With the development of science, people started to concern with more and more compli-cated engineering application. Thus, the hybrid system which contains simultaneously contin-uous and discrete variables comes to field of people’s vision. Many actual systems have sucha characteristics, such as sampling control systems, logic control systems, rigid mechanicalsystems with collision and reset control, robots, network systems and so on. The two kindsvariables in a hybrid system may be all dynamically appeared, it leads to that the research ismore complicated than the traditional control theory. It also show the theoretic significance forthe investigation of hybrid systems.The thesis considers several types of hybrid systems. Their stability and stabilization areresearched. The main contents are as follows.Chapter1is a survey. Firstly, the chapter sums up the recent development of the researchin the area of hybrid systems and gives several hot topics in this area. Secondly, the modelsof hybrid systems and mathematical tools used in the thesis are presented. These preliminariesprovide a foundation for the further investigation of the thesis. Finally, major works of thethesis are introduced.Chapter2considers the problem of ISS (input-state stability) for several hybrid systems.The time-varying pulse system is considered. At first, we deal with the system without input.Sufficient conditions for the asymptotic stability of the system are obtained. Then the con-clusion is extended to the system with input. Both ISS and exponential ISS are considered.Sufficient conditions are obtained by using Lyapunov theory. Then by using small gain theoryand Lyapunov method, we derive sufficient conditions for the system which is interconnectedby hybrid subsystems. Finally, the hybrid system whose subsystem may have time delay and isnot ISS is considered. In order to guarantee the stability of the whole system the dwell time be-tween the continuous subsystem and discrete subsystem is necessary to be considered. Severalsufficient conditions are established. Chapter3studies the stabilization of the hybrid system. At first, we transfer the uncertainswitch system into a, equivalent cascade form, then we apply backstepping method and adap-tive technique to design the stabilization law. The adaptive technique is used to approximatethe unmodeled dynamics. Comparing with the existing method, the design seems to allowmore uncertain in the model, the robustness is also increased. Then we consider the hybridsystem which contains pulse and uncertain parameters. An adaptive control design is given tostabilize the complex hybrid system. Several sufficient conditions are presented by using LMIto improve the robust stability. Finally, we apply CLF to deal with the stabilization of switchedhybrid system. The CLF is firstly introduced into switched system. The switched system isextended into differential inclusion and the Fillipov solution is adopted. Feedback laws aredesign for the stabilization and exponential stabilization, respectively, by using the CLF.Chapter4studies robust control and stabilization for the hybrid system with time de-lay. Firstly, uncertain impulse dynamic network system with time delay is considered. Byconstructing Lyapunov-Krasovskii function, the adaptive controller is designed, and some suf-ficient conditions for exponential stability of the system are established. Then this chapterdeals with stochastic hybrid system with time delay. We establish Ito formula for the stochasticimpulse system and derive some conditions for exponential stability of the stochastic impulsesystem with time delay. At last, the chapter considers the stabilization of the switched sys-tem with time delay. Adaptive controllers are designed for some special systems and then areextended to more general cases.At Chapter5, we summarize the study completed in the thesis, and present some mean-ingful problems for further studies. The main contributions of this thesis are three aspects listedas follows.1. The thesis extends the theory of ISS and small gain to the nonlinear impulse systemand the hybrid system. Several sufficient conditions are established. These conclusions containthe ISS for the impulse system, ISS and exponent ISS for the hybrid system. The function ofdwell time for the stability of those systems is firstly considered and the condition of the dwelltime for the stability is established.2. Stabilization of the switched system is researched by using adaptive technique andbackstepping method. We extend the range of the unknown parameters, but reserve the trackingof the switched system. The differential inclusion theory and Fillipov solution concept arefirstly applied to the nonlinear switched system. CLF method and adaptive control are used todesign feedback to stabilize the switched system. 3. The impulse system with time delay is considered in the thesis. By using LMI, robustadaptive control laws are obtained to guarantee the uniform boundedness. The conclusion isthen extended to the stochastic hybrid system with time delay.