Delay Dependent Stability Criteria For Linear Systems With Time Varying Delay In A Range

Abstract: Time delays are a common problem in many physical systems. Presence of delay often leads to instability and poor control performance. So study of stability of systems with time delay has gained much popularity. This paper is concerned with the stability analysis of systems with time delay. Time delay is assumed to be continuous time varying function and it belongs to a specified range. This states that the lower and upper bounds of the delay are assumed to be known. Here the upper delay bound is considered to be known and lower delay bound is considered to be zero. Using an appropriate Lyapunov functional, delay dependent stability criteria is proposed. Stability conditions are defined using Linear Matrix Inequalities (LMI). Effectiveness of the proposed method is demonstrated using a suitable numerical example.

Keywords: Time delays, Asymptotic stability, Lyapunov functional, Linear Matrix Inequalities.