Fuzzy descriptor systems and nonlinear model following control

TLDR

The fuzzy descriptor system framework encompasses regulation and servo control problems as special cases. This paper defines a fuzzy descriptor system, illustrates its construction, and proposes a nonlinear model‑following control strategy using twin parallel distributed compensations (TPDC) as a unified approach. The authors extend the Takagi‑Sugeno fuzzy model to a descriptor form, illustrate its construction, and employ linear matrix inequalities to design stable feedback gains, a common Lyapunov function, and TPDC‑based control. The study derives linear‑matrix‑inequality conditions for stability of the fuzzy descriptor system and demonstrates that the TPDC‑based nonlinear model‑following control achieves stable operation.

Abstract

This paper defines a fuzzy descriptor system by extending the ordinary Takagi-Sugeno (T-S) fuzzy model. Several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities (LMIs). We illustrate an example of defining the fuzzy descriptor system instead of the ordinary T-S fuzzy model. An LMI design approach is employed to find stable feedback gains and a common Lyapunov function. In addition, this paper presents a nonlinear model following control for the fuzzy descriptor system. A new parallel distributed compensation, the so-called "twin parallel distributed compensations" (TPDC) to realize the nonlinear model following control, is proposed. We present a design technique based on the TPDC. The proposed method is a unified approach to nonlinear model following control. It contains the regulation and servo control problems as special cases.