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The method of Implicit Lyapunov-Krasovski Functional (ILKF) for stability analysis of time-delay systems is introduced. Theorems on Lyapunov, asymptotic, (hyper) exponential, finite-time and fixed-time stability analysis using ILKF are presented. The hyper exponential stabilization algorithm for a time-delay system is presented. The theoretical result is supported by numerical simulation.
The problem of input-to-output stability for switched nonlinear systems is considered. Two approaches for switching between non-exponentially stable systems are proposed guaranteeing input-to-output stability for the switched system.
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