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| Received:November 14, 2006Revised:May 29, 2007 |
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| Robust stability and H-infinity control for uncertain discrete-time Markovian jump singular systems |
| Shuping MA, Chenghui ZHANG, Xinzhi LIU |
| (School of Mathematics and System Science, Shandong University, Jinan Shandong 250100, China; School of Computer Science and Technology, Shandong University, Jinan Shandong 250061, China; School of Control and Engineering, Shandong University, Jinan Shandong 250061, China; Department of Applied Mathematics, University of Waterloo, Waterloo Ontario N2L 3G1, Canada) |
| Abstract: |
| The robust stability and stabilization, and H-infinity control problems for discrete-time Markovian jump singular systems with parameter uncertainties are discussed. Based on the restricted system equivalent (r.s.e.) transformation and by introducing new state vectors, the singular system is transformed into a discrete-time Markovian jump standard linear system, and the linear matrix inequality (LMI) conditions for the discrete-time Markovian jump singular systems to be regular, causal, stochastically stable, and stochastically stable with °- disturbance attenuation are obtained, respectively. With these conditions, the robust state feedback stochastic stabilization problem and H-infinity control problem are solved, and the LMI conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper. |
| Key words: Discrete-time singular system Markovian jump system Robust stability and stabilization H-infinity control Linear matrix inequality(LMI) |
