Guaranteed Cost Control For A Class Of Uncertain Switched Descriptor Systems

As an important class of switched systems, the switched descriptor system is composed of a family of subsystems and the switching signal between them, but the subsystems are descriptor systems. Many problems must be taken into account, so the study of switched descriptor systems is very complex. The problem of the guaranteed cost control for uncertain switched descriptor systems is much more complicated. It not only makes the system satisfy the regularity and the stability in all the uncertainty, but also ensure the continuity of the system in switching signal, at the same time, its performance index is also confined to a given range. Based on the linear matrix inequality and the common Lyapunov functions, three related issues of guaranteed cost control for uncertain switched descriptor systems are mainly discussed in this paper.The main organization of this paper is as follows:Firstly, some introduction with respect to the switched systems, the descriptor systems and the guaranteed cost control are given briefly. Secondly, basic knowledge and common lemmas are considered. Thirdly, the main research results are discussed in Chapter3,4,5:(1) By considering the controller with an additive perturbation, the non-fragile guaranteed cost control of uncertain switched descriptor systems is studied for the quadratic performance functions. Based on common Lyapunov functions, the sufficient conditions under arbitrary switching laws are provided by two different methods and the form of the linear matrix inequality for the controller is also developed. Finally, a simulation example is given to illustrate the validity of the approach proposed.(2) Based on the effect of the nonlinear disturbance for the system performance index, the guaranteed cost control for uncertain switched descriptor systems with nonlinear disturbances is solved. When the regarded disturbance is fixed in a permissible range, the sufficient condition and the design approach for the existence of the guaranteed cost controller for the closed loop system under arbitrary switching laws are derived by the common Lyapunov functions and the linear matrix inequality. At last, a numerical example shows the effectiveness of the method via the LMI-box.(3) The guaranteed cost control for uncertain discrete switched descriptor systems with time delay is discussed for the quadratic performance functions. The sufficient condition of the existence of the guaranteed cost controller under arbitrary switching laws is obtained. Then, the design method of the controller is given by translating it into the form of the linear matrix inequality. In the end, a numerical example is employed to validate the design method.Lastly, the corresponding contents and some problems to be solved of this paper are expounded briefly in the summary and prospect.