Robust Analysis Of Neutral Systems With Time Delays

During establishing models for practical control systems, there are discrepancies between the system model and the practical problems which can be described as uncertainties of systems resulting from inevitable measurement error, various interference and unmodelled dynamics, and so on. In addition, there always exist time delays in the system. Time delays not only exist in the state, but also may appear in the state change rate, that is so called neutral systems with time delays. Uncertainty and time delays are important factors which affect the performance of neutral systems. Therefore, the research on uncertain neutral systems with time delays is an important and difficult part in the research on the problems of system control. In this paper the robust stability of neutral systems with time delays is investigated, assumed that the uncertainties in the system satisfy some conditions.1. The problem of the robust stability for neutral systems with discrete and distribution time delays is investigated. Firstly, by constructing appropriate Lyapunov functional combined with the analysis technique of the inequality, the condition of distributed-delay-dependent robust stability of the system is present. Then by constructing appropriate Lyapunov functional and introducing zero equations with free-weighting matrices, together with using linear matrix inequalities, discrete-delay-dependent and distributed-delay-dependent robust stability condition of the system is deduced. Those conditions can be translated into linear matrix inequalities. Finally, a number of examples are presented to validate the effectiveness of the proposed results.2. The problem of exponential stability for neutral systems with time-varying delays is investigated. By employing the Razumikhin-Lyapunov technique, the sufficient conditions of delay-independent exponential stability are obtained for both different initial state space which are continuous initial state space and continuously differentiable initial state space.