Robust quadratic control of discrete-time singular Markov jump systems with bounded transition probabilities

The quadratic 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 (LMIs) methods which guarantee that the closed-loop discrete-time singular Markov jump systems are regular, causal and 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.