Lyapunov–Krasovskii functionals for homogeneous time delay systems of neutral type

• Published in: International journal of robust and nonlinear control Vol. 32; no. 6; pp. 3251 - 3265
• Main Authors: Alexandrova, Irina V., Zhabko, Alexey P.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.04.2022
• Subjects: Asymptotic properties; homogeneous functions; Liapunov functions; Lyapunov–Krasovskii functionals; robust stability; systems of neutral type; Time delay systems; time delays
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5684

In this article, we present a general construction of Lyapunov–Krasovskii functionals for a class of neutral‐type time delay systems with a linear difference part and homogeneous right‐hand sides of degree strictly greater than one. Under an assumption that the corresponding difference matrix equation as well as a system with zero delays are asymptotically stable, the functionals allow proving delay‐independent asymptotic stability. They are based on the Lyapunov functions of the corresponding delay free systems and constitute a generalization of constructions presented recently for homogeneous systems of retarded type. The functionals are applied to the robustness analysis with respect to uncertainties at the right‐hand sides and at the difference term as well.