Finite-Time Stability and Stabilization for Continuous Systems with Additive Time-Varying Delays

This paper is centered on the problem of delay-dependent finite-time stability and stabilization for a class of continuous system with additive time-varying delays. Firstly, based on a new Lyapunov–Krasovskii-like function (LKLF), which splits the whole delay interval into some proper subintervals, a set of delay-dependent finite-time stability conditions, guaranteeing that the state of the system does not exceed a given threshold in fixed time interval, are derived in form of linear matrix inequalities. In particular, to obtain a less conservative result, we take the LKLF as a whole to examine its positive definite which can slack the requirements for Lyapunov matrices and reduce the loss information when estimating the bound of the function. Further, based on the results of finite-time stability, sufficient conditions for the existence of a state feedback finite-time controller, guaranteeing finite-time stability of the closed-loop system, are obtained and can be solved by using some standard numerical packages. Finally, some numerical examples are provided to demonstrate the less conservative and the effectiveness of the proposed design approach.

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