H∞ Control of Markovian Jump Systems with Incomplete Knowledge of Transition Probabilities

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An H∞ state-feedback controller for Markovian jump systems with incomplete knowledge of transition probabilities and input quantization is proposed. To derive the less conservative stabilization conditions, the conditions are developed into the second-order matrix polynomials of the unknown transition rate using an appropriate weighting method. Furthermore, the proposed controller not only accomplishes an H∞ performance but also removes the matched disturbances and the effect of input quantization. Two examples show the effectiveness of the proposed method.