Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov–Krasovskii functional approach

• Published in: Automatica (Oxford) Vol. 46; no. 5; pp. 949 - 952
• Main Authors: Zuo, Zhiqiang, Ho, Daniel W.C., Wang, Yijing
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.05.2010; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Criteria; Delayed systems; Derivatives; Exact sciences and technology; Functionals; Inequalities; Maximal Lyapunov–Krasovskii functional; Modelling and identification; Polytopes; Polytopic uncertainties; Reachable set; Time delay; Time delay systems; Uncertainty; Delayed systems; Maximal Lyapunov–Krasovskii functional; Reachable set; Polytopic uncertainties; Polytope; Set computation; Delay system; Reachability analysis; Reachability; Uncertain system; Integral equation; Delay time; Lyapunov function; Maximal Lyapunov―Krasovskii functional
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.02.022

This paper deals with the problem of reachable set estimation for time delay systems subject to both polytopic parameter uncertainties and bounded peak inputs. The maximal Lyapunov–Krasovskii functional is constructed as the pointwise maximum of a family of Lyapunov–Krasovskii functionals. Each functional corresponds to a vertex of uncertain polytope. Some criteria bounding the reachable set are derived. This approach shows great advantages over the traditional methods based on the common Lyapunov functionals. By introducing a modified integral inequality, the limitation imposed on the derivative of time delay being less than one is relaxed. Furthermore, the obtained results involve less computational burden when the number of vertices of the polytope is small. Two examples are given to illustrate the theoretical results.