Non-fragile sliding mode control of discrete-time T-S fuzzy singular system via a previewable approach.

In this paper, the non-fragile sliding mode control (SMC) problem is discussed for discrete-time T-S fuzzy singular systems (TSFSSs) by employing a previewable approach. Firstly, an augmented system incorporating the tracking error and preview information is formulated based on lengthes of preview information. Secondly, a fuzzy non-fragile sliding mode surface (SMS) is established for augmented error system based on both additive and multiplicative perturbations, and the sufficient conditions for sliding mode dynamics to be H ∞ admissibility are derived by designing suitable Lyapunov functionals. Then, a non-fragile preview SMC law is determined to ensure that the reachability condition is met. Finally, the example is offered to demonstrate that the given preview SMC law can substantially improve the tracking performance of the original output.