LMI-based Approach of Global Exponential Robust Stability for a Class of Uncertain Distributed Parameter Control Systems with Time-varying Delays

Abstract: In this paper, the global exponential robust stability analysis problem is considered for a class of uncertain distributed parameter control systems with time-varying delays. The uncertain parameters are gen-erated from modeling errors as well as parameter variations in the systems. The purpose of the problem addressed is to derive some easy-to-test conditions such that the dynamics of the uncertain system is globally exponentially robustly stable. By employing a new Lyapunov-Krasovskii functional, a linear matrix inequal-ity (LMI) approach is developed to establish the desired sufficient conditions and therefore global exponential robust stability for the uncertain distributed parameter control systems with time-varying delays can be eas-ily checked by utilizing the numerically efficient Matlab LMI toolbox. A numerical example is exploited to show the usefulness of the derived LMI-based stability conditions