Implicit Lyapunov-Krasovski Functionals for time delay systems

Abstract

The method of Implicit Lyapunov-Krasovski Functional (ILKF) for stability analysis of time-delay systems is introduced. Theorems on Lyapunov, asymptotic, fiite-time, fixed-time and (hyper-)exponential stability analysis using ILKF are presented. The hyper exponential stabilization algorithm for a time-delay system is developed. The theoretical results are supported by numerical simulations.