A Novel Design of Nonfragile Observer-Based Controller for Discrete Fuzzy Descriptor Systems via Sliding-Mode Approach

This brief devotes on the design of a new robust nonfragile observer-based controller for discrete T-S fuzzy descriptor systems (TSFDSs) based on sliding mode approach. Based on a novel structure, a nonfragile state observer is synthesized so that it is easy to implement. Novel $H_{\infty }$ -admissibility criteria are derived for the sliding mode systems with the removal of non-strict constrains. The fuzzy sliding mode surface is proposed with fully considering the effect of the difference matrix $E$ on the controller design. Furthermore, according to reaching condition, the nonfragile observer and sliding mode controller are co-designed for discrete TSFDSs based on strict linear matrix inequality (LMI). Finally, the efficiency of the proposed approach is illustrated by a nonlinear circuit system.