Uncertain Robust Control Of The Lurie Control Systems

In this paper, the problem of robust control for the uncertain Lurie control systems is studied, and the main purpose is to discuss the robust absolute stability conditions for the uncertain Lurie control systems with time-delay and non-time-delay. On one hand, the results are expanded into the case that the uncertain Lurie control system is the control system with the various kinds of uncertainty; on the other hand, some results obtained are improved and perfected. Firstly, the problem of robust control for the uncertain Lurie control systems is studied where the uncertain matrices are unstructured uncertainty, highly structured uncertainty, matrix polytope uncertainty and norm bounded uncertainty .The relevant determined conditions by which the systems are robust absolute stabilities are obtained by using Lyapunov functional method and combining essential matrix theory and corresponding inequality technique. Then some examples are given to illustrate them. Secondly, the problem of robust control for the uncertain Lurie control systems with time-delay is studied and the determined conditions by which the systems are robust absolute stabilities are derived by constructing right Lyapunov functional, some examples are given to illustrate them. Thirdly, the problem of robust absolute stability is studied for the uncertain Lurie control systems with multiple time-delay. The sufficient conditions of robust absolute stability under the unstructured uncertainty assumption are derived by using Lyapunov functional method and Razumikhin theorem. The relevant example is given to illustrate it.