Robust Passive Control For Uncertain Singular Systems

In practical systems, the factors including measure error, change of input condition, abnormal work of sensor and actuator and external disturbance bring about the appearance of uncertainties. So, the robust passive control problem of uncertain singular systems is mainly studied in this paper. The main contents of the paper are as follows:First of all, the passive control problem for a class of multi-time delay uncertain singular systems is investigated. By using the method of linear matrix inequality (LMI), a sufficient condition is firstly presented for the multi-time-delay uncertain singular system to be passive. Then the existence condition of a passive state feedback controller is given and the explicit expression of the controller is derived in terms of the solution of LMI. At last, a numerical example is simulated by utilizing Matlab LMI toolbox, and the result demonstrates the validity and effectiveness of the proposed method.Then, the robust passive control problem for a class of linear systems with time-varying multiple time-delays uncertain systems is studied. Based on LMI methods and the Lyapunov function, passive condition of the system is obtained, and a passive robust memory-less state feedback controller design method is given. By examplifying, the feasibility of the theorem is verified.Next, the robust passive control problem for a class of time-varying uncertain singular systems with state delay and input delay is studied. The uncertainty is norm-bounded, but does not need to meet the matching condition. Based on LMI methods and the generalized Lyapunov function, the passive condition of time-varying delay uncertain singular systems is obtained. Meanwhile, the design of a memory-less feedback controller is solved, making the closed-loop system is strictly passive. The result demonstrates the validity of the result.Finally, the problem of strictly passive realness for uncertain discrete linear singular systems is investigated by using the linear matrix inequality approach. As to a class of linear systems in the right conditions, a new sufficient condition is presented for singular systems to be regular, causal, stable and strictly passive. The obtained condition is formulated in terms of strict linear matrix inequality, which does not involve the system state matrix decomposition.