Reachable Set Estimation and Decentralized Controller Design for Large-Scale Nonlinear Systems With Time-Varying Delay and Input Constraint
This paper investigates the problem of reachable set estimation and decentralized controller design for large-scale nonlinear systems, where time-varying delays and nonlinearities appear in interconnections connected to other subsystems. The Takagi–Sugeno model is used to describe each nonlinear subsystem. The aim of this paper is to design a decentralized state-feedback fuzzy controller such that the reachable set of the resulting closed-loop system with input constraint is bounded by an intersection of ellipsoids. First, a model transformation is proposed to reformulate the closed-loop system as several feedback interconnections with extra inputs and outputs. Then, based on a combined application of the Lyapunov–Krasovskii functional and the scaled small-gain theorem, the input–output approach is developed for the reachable set estimation and synthesis. Several conditions for the existence of a decentralized state-feedback fuzzy controller that ensures an ellipsoidal bound of reachable sets for the closed-loop system with input constraint are derived in terms of linear matrix inequalities. Finally, two numerical examples are given to validate the effectiveness of the proposed strategy.