Robust stability and H∞ control for uncertain discrete Markovian jump singular systems with mode‐dependent time‐delay |
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Authors: | Shuping Ma Chenghui Zhang |
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Affiliation: | 1. School of Mathematics and System Science, Shandong University, Jinan 250100, China;2. School of Control and Engineering, Shandong University, Jinan 250061, China |
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Abstract: | The robust stochastic stability, stabilization and H∞ control for mode‐dependent time‐delay discrete 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 standard linear system, and delay‐dependent linear matrix inequalities (LMIs) conditions for the mode‐dependent time‐delay discrete Markovian jump singular systems to be regular, causal and stochastically stable, and stochastically stable with γ‐disturbance attenuation are obtained, respectively. With these conditions, robust stabilization problem and robust H∞ control problem are solved, and the LMIs sufficient conditions are obtained. A numerical example illustrates the effectiveness of the method given in the paper. Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | discrete Markovian jump singular system time‐delay system delay‐dependent robust stability and stabilization H∞ control |
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