Robust Control Of Several Classes Of Switch Systems With Time Delays

As an important class of hybrid systems, the switched systems can be used to model many actual complex control systems with continuous dynamics and discrete dynamics in industrial processes; Multi-controller switching control technology can effectively cope with highly complex systems or systems with large uncertainties and the progress of computer control technology immensely promote the study of control systems. Time delay presences widespread in various industrial processes, and is the main source of instability and poor performances of control systems, so the study on time delay systems have received considerable attention by many researchers, and became a hot issue in control areas and control engineering. Time-delay switched systems is a class of complex dynamic systems with the interaction of continuous dynamics and discrete dynamics and time delays which make the analysis and control of switched systems difficult, hence the study on robust control of switched systems with time delays is of great significance. Based on the switched Lyapunov-Krasovskii functions, linear matrix inequality technology, the cone complementary linearization algorithm, this dissertation investigates the asymptotic stability of two classes of linear discrete-time switched system with time-varying delays under a given H_∞performance, construct the switched feedback controllers which meet the given H_∞performance. Finally, several numerical examples are given to illustrate the correctness and validity of the proposed results. The main work and research results of this thesis lie in the following:Chapter 3 investigates the robustly stability and state-feedback stabilization for a class of linear discrete-time switched systems with time-varying delays. The system matrixes of all sub-systems, are norm bounded and time-varying. By applying full switched Lyapunov-Krasovskii function method, two sufficient conditions constructing the state-feedback controller are given for the underlying system under arbitrary switched signals. All the conditions are delay-dependent, the first condition is in terms of LMI, and the second one is nonlinear, an iterative algorithm is given by cone complementary linearization algorithm. The obtained controller not only guarantee the corresponding closed-loop system asymptotically stable, but also a prescribed H_∞noise-attenuation level bound is guaranteed. Finally, a numerical example is given to compare the result with previous results in [9] and illustrate our results with less conservative, another example is given to compare the two methods of constructing state-feedback controller and illustrate the first method is better than the second one.Chapter 4 concern with the output-feedback control of uncertain linear discrete-time switched systems with multiple time-varying delays, the uncertainty is norm-bounded. By applying switched Lyapunov-Krasovskii function method, the sufficient conditions of constructing the output feedback controller of multiply time-delay switched systems under arbitrary switch signals is given. The obtained controller not only guarantee the corresponding closed-loop system asymptotic stable, but also a prescribed H_∞noise-attenuation level bound is guaranteed. The obtained condition is delay-dependent but nonlinear. The cone complementary linearization algorithm is used to transform the feasibility problem of the nonlinear matrix inequalities into a nonlinear program problem subject to linear matrix inequalities,and an iterative algorithm is given to solve this nonlinear program problem.