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| Received:March 14, 2003Revised:December 26, 2003 |
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| Robust H_∞ control for discrete-time polytopic uncertain systems with linear fractional vertices |
| Shaosheng ZHOU, James LAM, Shengyuan XU |
| (Institute of Automation, Qufu Normal University, Qufu Shandong 273165, China; The State Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, China; Department of Mechanical Engineering, University of Hong Kong, Hong Kong; Department of Automation, Nanjing University of Science and Technology, Nanjing Jiangsu 210094, China) |
| Abstract: |
| The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results. |
| Key words: Discrete-time systems H∞, control Linear matrix inequality Uncertain systems |
