Linear Delay Systems Of Several Robust Control Problem

The studying of singular systems with time-delay attracts considerable attention in recent years, for such kind of systems is more general and widely used. The research on linear singular systems with time-delay is of theoretical and practical importance. In this paper, robust H_∞ control, robust stabilization and robust guaranteed cost control problems about singular systems with time-delay in state are investigated, and delay-dependent stability is also discussed.First, the H_∞ static output -feedback controller with memory is researched. A sufficient condition that can make closed-loop system admissible and satisfies H_∞ performance index is obtained, the static output feedback JH_∞ controller, which satisfies the requirement of design, is obtained by solving an LMI. Then the result of system's state with uncertainty is also obtained. Then robust H_∞ control of system state with uncertainty is discussed. The similar controller is also designed.Next, the problem of robust stabilization for uncertain singular systems with time-delay is investigated. For a kind of uncertainty, a design method of robust feedback controller, which shows that the proposed state feedback systems are of robustness in the presence of all admissible parameter perturbations, is put forward by LMI.Third, the problem of guaranteed cost control of uncertain linear singular systems with time-delay in state is solved. The uncertain linear singular system with time-delay under consideration contains a more practical and general faults model of actuator. The quadratic cost function is employed for measuring the system performance. Linear state feedback law constructed by the solutions of LMIs can make the closed-loop systems admissible and sufficient conditions for existence of the controller that guarantees an upper bound of system performance are given based on LMIs .Finally, a new integral inequality method is proposed to discuss delay-dependent stability of linear singular systems with time-delay in state. An integral inequality based on quadratic term is formulated by Park inequality, then using Lyapunov-Krasovskii functional method, delay-dependent stability is obtained based on matrix inequalities. An example is given to illustrate that the result here is of less conservation.