Observer-Based Adaptive Sliding Mode Control for T-S Fuzzy Singular Systems

This paper investigates the problem of adaptive ${H}_{\infty}$ sliding mode control (SMC) for a class of nonlinear systems via Takagi–Sugeno (T–S) fuzzy model approach. The input matrices and output matrices in all local linear systems are different. A novel observer is designed to estimate the unmeasured states. Based on such an observer, the control input is only appeared in the T–S fuzzy singular system and error system. A new integral sliding surface is put forward to match the characteristic of T–S fuzzy singular system with different input and output matrices. Based on the new integral sliding surface, a new adaptive SMC scheme is designed to guarantee the admissibility of the T–S fuzzy singular system with ${H}_{\infty}$ performance and the reachability of the T–S fuzzy integral sliding surface. A simulation result is presented to illustrate the effectiveness and feasibility of the developed observer-based SMC design method.