INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2003; 13:1017–1033 (DOI: 10.1002/rnc.750) Refined discretized Lyapunov functional method for systems with multiple delays Keqin Gu n,y Department of Mechanical and Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville, IL 62026-1805, USA SUMMARY The previously proposed discretized Lyapunov functional method for systems with multiple delay is refined using variable elimination and Jensen inequality. The resulting new stability criterion is simpler. Numerical examples indicate that the new method is much less conservative for a given discretization mesh. Copyright # 2003 John Wiley & Sons, Ltd. KEY WORDS: Lyapunov–Krasovskii functional; time-delay system 1. INTRODUCTION Time-delay systems are frequently encountered in engineering, biological, economical, and other dynamical systems [1]. In the wake of intensive research on the robust stability and control theory in the 1980s, the stability and control of time-delay systems have received renewed interests. The development of efficient computational algorithm for non-smooth convex optimization problem, which made it possible to efficiently solve linear matrix inequalities (LMI) [2], inspired intensive activities to formulate such problems in an LMI form. The stability problem of systems with multiple delays, especially when the delays are incommensurate, without considerable conservatism and with practically computable algo- rithm, presents challenge for both frequency domain approaches and time-domain approaches. See References [3–5] for an overview. Gu [6] proposed a discretized Lyapunov functional method for such a problem, which is an extension to the single delay case originally proposed in Reference [7]. This paper attempts to simplify the formulation and make the criterion less conservative using the variable elimination technique and Jensen inequality, parallel to the single delay case discussed in Reference [8]. As a result, the stability criterion is significantly Received 20 January 2001 Revised 23 October 2001 Published online 31 March 2003 Accepted 15 July 2002 Copyright # 2003 John Wiley & Sons, Ltd. n Correspondence to: Dr. Keqin Gu, Department of Mechanical & Industrial Engineering, Southern Illinois University at Edwardsville, Edwardsville, Illinois 62026-1805, U.S.A y E-mail: kgu@siue.edu Contract/grant sponsor: National Science Foundation; contract/grant number: INT-9818312