Integral sliding mode H∞ control for T-S fuzzy singular Markovian jump systems with uncertainties in the derivative matrices

The paper investigates sliding mode control (SMC) for a class of T-S fuzzy singular Markovian jump systems (SMJSs) with uncertainties in the derivative matrix. To overcome the challenges posed by uncertainties in the derivative matrix, an augmented system is constructed, and a fuzzy integral sliding function is designed for this augmented system. Then, within the framework of linear matrix inequalities (LMIs), a sufficient condition is provided to ensure that the sliding mode dynamics is stochastically admissible and has an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> disturbance attenuation performance. In addition, an appropriate sliding mode control law is designed to guarantee that the reachability condition is satisfied. Finally, the effectiveness of the proposed method is validated through a simulation example.