Research Of Quadratic Stabilization Problems Of Uncertain Singular Switched Systems

This paper focuses on the research of quadratic stabilization problems of uncertain singular switched systems. The uncertainties of systems describe problems accurately, which reflects the existence of the variation of system parameters and disturbance. In addition, in real life, the phenomenon of time-delay is common. Therefore, to solve the problem, this paper also studies the uncertain singular switched systems with time-delay.The main contents of this paper are as follows(1) Firstly, for the uncertain singular systems, we study the existence of the observer which can make the systems quadratic stabilization, and give a sufficient condition of the existence of the observer. At last, a numerical example is given to illustrate the effectiveness of the condition;(2) Secondly, for the uncertain singular switched systems, the Hx guaranteed cost problems of the systems are investigated. And based on common Lyapunov function approach, and linear matrix inequalities approach, a necessary and sufficient condition of the existence of the H guaranteed cost controller is given, and the corresponding switching law is given, too. At the same time, the algorithm which makes the cost function upper bound of the controller smallest is given. At last, a numerical example is given to illustrate the effectiveness of the condition;(3) Next, the resilient H∞ problems of the uncertain singular time-delay switched systems are investigated. And while the addition perturbation and the multiplication perturbation are exist, the sufficient conditions of the existence of the corresponding resilient H∞ controllers are given respectively. At the same time, the corresponding switching laws are given, too. At last, numerical examples are given to illustrate the effectiveness of the conditions respectively;(4) Finally, the resilient H∞ guaranteed cost problems of the uncertain singular time-delay switched systems are investigated. And while the addition perturbation and the multiplication perturbation are exist, the sufficient conditions of the existence of the corresponding resilient H∞ controllers are given respectively. At the same time, the corresponding switching laws are given, too. At last, numerical examples are given to illustrate the effectiveness of the conditions respectively.