Parameter-Dependent Lyapunov Function Approach to Stability Analysis and Design for Uncertain Systems with Time-Varying Delay

This paper is devoted to stability analysis and synthesis of uncertain systems with time-varying delay. A new parameter-dependent Lyapunov function analyzing approach is proposed to reduce the conservativeness in delay-independent and delay-dependent stability analysis for the polytopic systems with time delay. Some new stability conditions are developed for the systems based on the Razumikhin stability theorem. A design method for general state feedback controllers is then proposed for the polytopic systems with time delay by the LMIoptimi zation based approach. Numerical examples are used to demonstrate the effectiveness of the proposed design approach.