New results on sliding mode control for polynomial fuzzy singular systems with time-varying delay

This article focuses on the problem of sliding mode control (SMC) for polynomial fuzzy singular systems with the matched uncertainty, time-varying delay and different control input matrices. An integral sliding surface with different control input matrices and polynomial matrices is established. The existence of the equivalent controller can be determined according to the given sum-of-squares conditions. By choosing an appropriate augmented Lyapunov-Krasovskii functional and utilizing a generalized free-matrix-based integral inequality, a less conservative admissibility condition of sliding mode dynamics is proposed in the form of sum-of-squares. It is noteworthy that due to the choice of augmented Lyapunov-Krasovskii functional, the traditional methods cannot transform the nonlinear terms in the admissibility condition of sliding mode dynamics into linear terms. Here, several inequalities are introduced to overcome this difficulty. Furthermore, the SMC law is proposed to ensure the reachability of the sliding surface. The simulation results show that the proposed method is less conservative and effective.