Adaptive Robust H∞ Sliding Mode Control for Singular Systems with Time-varying Delay and Uncertain Derivative Matrix

This paper considers the problem of sliding mode control (SMC) design for a class of nonlinear singular systems with time-varying delay and uncertainties, especially with uncertainties in the derivative matrix. By taking uncertainties of the derivative matrix into account, the state augmentation transformation is constructed such that uncertainties of the derivative matrix are eliminated. Then an appropriate integral-type sliding surface function is designed. And the resulting sliding mode dynamics is an uncertain singular time-varying delay system. A delaydependent sufficient condition which guarantees the sliding mode dynamics to be admissible with H∞ performance is established. A new version of stabilization solvability condition is then proposed in terms of linear matrix inequality (LMI), which determines the undetermined parameter K in both the sliding surface function and the SMC laws. Moreover, two distinctive controllers (i.e., an SMC law and an adaptive SMC law) are synthesized such that the finite-time reachability of the predesigned sliding surface can be ensured. Finally, simulation examples are given to demonstrate the effectiveness and the merits of the proposed theory.