Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach

TLDR

Takagi‑Sugeno fuzzy models represent complex nonlinear systems by combining fuzzy sets with linear input/output submodels. This work extends the TS fuzzy model framework to analyze stability and design controllers for continuous and discrete‑time nonlinear systems with time delay. The authors formulate time‑delay TS fuzzy models, derive Lyapunov‑Krasovskii stability conditions, and propose a stabilization strategy using fuzzy state‑feedback and observer‑based controllers, with gains obtained by solving coupled linear matrix inequalities and demonstrated on a CSTR example.

Abstract

Takagi-Sugeno (TS) fuzzy models (1985, 1992) can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input/output (I/O) submodels. In this paper, the TS fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete-time nonlinear systems with time delay. The TS fuzzy models with time delay are presented and the stability conditions are derived using Lyapunov-Krasovskii approach. We also present a stabilization approach for nonlinear time-delay systems through fuzzy state feedback and fuzzy observer-based controller. Sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities. An illustrative example based on the CSTR model is given to design a fuzzy controller.