INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2001; 11:1455–1468 (DOI: 10.1002 /rnc.669) IQC robustness analysis for time-delay systems Myungsoo Jun 1,z and Michael G. Safonov 2, * ,y 1 Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, U.S.A 2 Department of Electrical Engineering–Systems, University of Southern California, Los Angeles, CA 90089-2563, U.S.A SUMMARY Stability robustness of systems with uncertain time delays is considered. A new delay-dependent state-space stability criterion is formulated in the form of an easily checked LMI condition. Two applications of the main result are presented, one with only time-delay uncertainty and one with both delay and parametric uncertainty. Copyright # 2001 John Wiley & Sons, Ltd. KEY WORDS: time-delay; stability; robustness; linear matrix inequality (LMI) 1. INTRODUCTION Stability criteria for time-delay systems tend to fall into one of two categories according to their dependence upon delay size, delay-dependent [1,2] or delay-independent [3–5]. Delay- independent criteria provide conditions for stability without regard for the size of the time delays. They tend to be more conservative than delay-dependent criteria which may exploit prior knowledge of upper-bounds on the amount of time-delay. Time delays are usually assumed to be unknown but constant and belonging to a certain range, that is, HðsÞ¼ H 1 ðsÞe st ; 04t4% t where HðsÞ is the transfer function of a system with uncertain time-delays t and H 1 ðsÞ is the nominal transfer function with t=0. The time delay is an example of real parametric uncertainty, with the uncertainty entering nonlinearly. Nevertheless, uncertain time-delays can be treated as structured uncertainties and analysed using robust control theory [6–9]. Many methods of robust control analysis have been shown to fall within the framework of the integral quadratic constraints (IQC’s) [10]. Fu et al. [11] and Jun et al. [12] provided delay- dependent results for robust stability using the IQC approach and the linear matrix inequalities (LMIs) technique, which gave an estimate of the maximum time-delay which preserves robust stability. Copyright # 2001 John Wiley & Sons, Ltd. *Correspondence to: Micheal G. Safonov, Department of Electrical Engineering}Systems, University of Southern California, Los Angeles, CA 90089-2563, USA. y E-mail: msafonov@usc.edu z This research was done while the author stayed at University of Southern California. Contract/grant sponsor: AFOSR; contract/grant members: F49620-98-1-0026 and F49620-01-1-0302