Guaranteed cost control of uncertain discrete‐time singular Markov jump systems with indefinite quadratic cost

The guaranteed cost control problem for discrete‐time singular Markov jump systems with parameter uncertainties is discussed. The weighting matrix in quadratic cost function is indefinite. For full and partial knowledge of transition probabilities cases, state feedback controllers are designed based on linear matrix inequalities method which guarantee that the closed‐loop discrete‐time singular Markov jump systems are regular, causal and robust stochastically stable, and the cost value has a zero lower bound and a finite upper bound. A numerical example to illustrate the effectiveness of the method is given in the paper. Copyright © 2010 John Wiley & Sons, Ltd.

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