A Delay Decomposition Approach to Delay-Dependent Robust Passive Control for Takagi–Sugeno Fuzzy Nonlinear Systems

This paper is concerned with the problem of delay-dependent robust passive control for a fuzzy nonlinear system with time-varying delays. A Takagi–Sugeno fuzzy model approach is exploited to design a passive control for nonlinear systems with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov–Krasovskii functionals (LKFs) are constructed on these intervals. Employing these new LKFs, a new robust passive control criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of the time delay. We also design a state feedback controller that guarantees a robustly strictly passive closed-loop system for all admissible uncertainties. Finally, two numerical examples are given to illustrate the effectiveness of the developed techniques.