Finite-time stability analysis and stabilization for uncertain continuous-time system with time-varying delay

Abstract

The problem of finite-time stability for a class of continuous-time system with norm-bounded uncertainties and time-varying delay is studied in this paper. The original system is firstly transformed into two interconnected subsystems. In order to extract the time-varying term of time delay, a two-term approximation of time-varying delay is used. By using the delay-dependent Lyapunov–Krasovskii-like functional and the method of linear matrix inequality (LMI), sufficient conditions for finite-time stability are derived. The derived conditions can analyze the finite-time stability of system and calculate the upper bound of time delay. In order to stabilize unstable system, the state-feedback and output-feedback controller are respectively designed. Results of numerical examples show the effectiveness of the proposed approach.