Sufficient Conditions for Exponential Stabilization of Linear Distributed Parameter Systems with Time Delays

摘要

The framework of Lyapunov-Krasovskii functions is the most popular approach for studying the problem of stability analysis and synthesis for time-delay systems. In this framework, this paper addresses the exponential stabilization problem of a class of linear distributed parameter systems with time delays described by partial differential-difference equations (PDdEs). Both delay-independent and delay-dependent design methods are subsequently developed by constructing two integral types of Lyapunov-Krasovskii functions and introducing a new form of Jensen's inequality, and presented in terms of a standard linear matrix inequality (LMI). Finally, the effectiveness and merit of the proposed design method are demonstrated by a numerical example.