Reachable set estimation and dissipativity for discrete-time T–S fuzzy singular systems with time-varying delays

Abstract

This paper studies the problems of reachable set estimation and dissipativity analysis for a class of nonlinear singular system with time-varying delays and bounded input disturbances. The nonlinear singular system is modeled by Takagi–Sugeno (T–S) fuzzy singular delay system. Firstly, based on new Lyapunov–Krasovskii functional, in which the difference of triple-summable terms and both the upper and the lower bound of time-varying delays are considered, and by using the free-weighting matrix technique, reciprocally convex combination approach, a new delay-dependent reachable set estimation and dissipativity condition is obtained. Furthermore, the derived condition can be converted into linear matrix inequalities (LMIs), and it can guarantee the reachable set to be bounded by the intersection of ellipsoids and the T–S fuzzy singular delay system is strictly (G1,G2,G3)−δ̃−dissipative. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained results in this paper.