Segmentation Systems And Section Delay Systems H_ ¡Þ Controller Design

The dissertation mainly deals with the robust H_∞ control problem of piecewise system and piecewise time-delay system. There are four chapters in this dissertation.In Chapter 1, we introduce the development of robust control, H_∞ control and LMI approach. Then the application of piecewise systems is given. Finally, the main work of this dissertation and the used notations are listed.In chapter 2, the robust H_∞ control problem for uncertain continuous-time piecewise systems is investigated. The uncertainties of the system under consideration are expressed in a linear fractional form. By using piecewise continuous Lyapunov function, a sufficient condition on robust stability with H_∞ norm bound is obtained. Moreover, a state feedback controller is developed to guarantee the closed-loop system being robustly stable with H_∞ norm bound. Aiming at the nonlinear terms and the equality constraints about the unknown variables in the sufficient conditions, we utilize the cone complementary linearization technique [23-25] and convert the solving for controllers to the non-convex optimization problems. And then the cone complementarity linearization iterative algorithms are proposed to design the desired controllers. Finally a numerical example is given to illustrate the application of the proposed approach.Chapter 3 is devoted to the problem of robust H_∞ control for continuous-time piecewise linear time-delay systems by using piecewise continuous Lyapunov function. The uncertainties of the systems under consideration are expressed in a linear fractional form. By utilizing two classes of slash variables, a strict linear matrix inequality approach is developed to obtain delay-dependent robust stability condition with H_∞ norm bound. Moreover, a state feedback controller is developed to guarantee the closed-loop system being ro-bustly stable with H^ norm bound. Aiming at the nonlinear terms and the equality constraints about the unknown variables in the sufficient conditions, we utilize the cone complementary linearization technique and convert the solving for controllers to the non-convex optimization problems. Finally two numerical examples are given to illustrate the application of the proposed approach.