Observer-based sliding mode control for discrete-time nonlinear system with time-varying delay

This work deals with the design observer-based sliding mode control for discrete-time Takagi–Sugeno fuzzy models with time-varying delay and subject to measurement noises. The sliding surface is developed by introducing the state and input vectors to overcome the restrictive assumption in most existing sliding mode control schemes which forces the input matrices of all linear subsystems to be equal. Sufficient stability conditions of the error system and sliding mode dynamics with disturbance attenuation level are developed using the augmented Lyapunov–Krasovskii functional and free-weighting matrix. Finally, a simulation example is presented to demonstrate the efficiency of the proposed results.