Robust stabilisation for a class of stochastic T–S fuzzy descriptor systems via dynamic sliding‐mode control

Abstract

In this study, the authors research the problem of robust stabilisation for a class of stochastic Takagi–Sugeno (T–S) fuzzy descriptor systems via dynamic sliding mode control technique. In the majority of stochastic T–S fuzzy sliding-mode control approaches, two restrictive assumptions are required, one is every subsystem's input matrix is identical, the other is the product of the sliding-mode gain and the stochastic perturbation matrix must be zero. In order to eliminate two restrictive assumptions, we put forward a dynamic sliding-mode control technique for a class of stochastic T–S fuzzy descriptor systems. A criterion is established according to linear matrix inequalities, it guarantees that the stochastic T–S fuzzy descriptor systems with the mismatched uncertainty and disturbance are stochastically admissible and strictly robust dissipative. Moreover, a dynamic sliding-mode controller ensures the reachability of the system trajectories to the predefined sliding surface in finite time. In the end, the technique is applied to an inverted pendulum model to demonstrate the merit and effectiveness of the proposed methods.