Adaptive sliding mode control for semi‐Markov jump uncertain discrete‐time singular systems.

This note is devoted to the analysis of adaptive sliding mode control of H∞$$ {}_{\infty } $$/passivity of semi‐Markov jump discrete‐time uncertain singular systems. We consider the constraints of parameter uncertainties, unknown nonlinear functions, and external disturbances throughout the model. Firstly, a novel mode‐independent sliding mode surface is constructed, then the sliding mode dynamic equation under the equivalent controller is obtained. Secondly, by introducing virtual points, several sufficiency criteria are derived for the sliding mode dynamic ensuring H∞$$ {}_{\infty } $$/passive performance and stochastic admissibility with linear matrix inequalities form. Thirdly, the state trajectory can be driven into a switching band containing the origin by adaptive sliding mode control techniques. Finally, the effectiveness of our findings is demonstrated by comparing existing strategies with three simulation examples. [ABSTRACT FROM AUTHOR]