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Finite-time stability analysis and stabilization for uncertain continuous-time system with time-varying delay. (English) Zbl 1307.93337
Summary: 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.

##### MSC:
 93D15 Stabilization of systems by feedback 93D30 Lyapunov and storage functions 93C15 Control/observation systems governed by ordinary differential equations
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