Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay |
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| Authors: | Zhuo Zhang Zexu Zhang Hui Zhang Bo Zheng Hamid Reza Karimi |
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| Institution: | 1. Deep Space Exploration Research Center, School of Astronautics, Harbin Institute of Technology, 150080, China;2. Scientific Research Academy, Shanghai Maritime University, Shanghai 201306, China;3. Department of Engineering, Faculty of Engineering and Science, University of Agder, Grimstad, Norway |
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| Abstract: | The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-term approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method. |
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