Limited Time Switching Systems With Time Delay Stability Study

A switched system is composed of an indexed family of subsystems described by con-tinuous or discrete-time dynamics and a rule orchestrating the switching between them.Switched systems have strong engineering background in various areas and are often usedas an unifed modeling tool for a great number of real-world systems such as power elec-tronics, chemical processes, mechanical systems, automotive industry, aircraft and air trafccontrol and many other felds. Switched systems with time delay are referred to as switchedtime-delay systems. In recent years, the stability problem of switched systems, especially ofswitched time-delay systems, has been widely investigated in the control community. Mostof the results in the literature are focused on Lyapunov stability. Few results have beenreported in literature on fnite-time stability, especially under asynchronous switching, ofswitched time-delay systems so far. This motivates the present study.The thesis mainly probes into the H_∞fnite-time boundedness and fnite-time stabiliza-tion problems of switched delay systems including discrete-time and continuous-time ones.More specifcally, the main contributions are listed below:In the second section, the problem of H_∞fnite-time boundedness is dealt with for aclass of discrete-time switched time-delay systems with nonlinear uncertainties. Firstly, byintroducing new Lyapunov-Krasovskii functionals and using the average dwell time method,a delay-dependent sufcient condition is developed, which guarantees that the given systemis (uniformly) fnite-time bounded. Then, based on the sufcient condition, a state feed-back controller is developed to ensure the resulting closed-loop system to be (uniformly)H_∞fnite-time bounded. All the conditions are presented in terms of strict linear matrixinequalities(LMIs), which can be easily checked by using recently developed algorithms insolving LMIs. Finally, a numerical example is provided to demonstrate the efectiveness ofthe main results.In the third section, the problem of fnite time stabilization under asynchronous switch-ing is dealt with for a class of switched time-delay systems with nonlinear uncertainties.Firstly, the nonlinear uncertainties are transformed into the linear time-varying forms viathe diferential mean value theorem under some assumptions. Secondly, by applying theaverage dwell time method and convexity principle, a fnite-time stability condition for theunforced switched time-delay system is frstly established. Finally, an asynchronous switch-ing state feedback controller is designed which renders the considered system fnite-time stable. Two numerical examples are provided to show the efectiveness of the developedresults.