Parameterized linear matrix inequality techniques in fuzzy control system design

This paper proposes different parameterized linear matrix inequality (PLMI) characterizations for fuzzy control systems. These PLMI characterizations are, in turn, relaxed into pure LMI programs, which provides tractable and effective techniques for the design of suboptimal fuzzy control systems. The advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations.

I. Introduction

The well-known Tagaki-Sugeno (T-S) fuzzy model [13] is a convenient and flexible tool for handling complex nonlinear systems [11], where its consequent parts are linear systems connected by IF-THEN rules. Suppose that is the state vector with dimension is the control input with dimension , and are the disturbance and controlled output of the system with the same dimension , and denotes the number of IF-THEN rules, where each th plant rule has the form

$$\begin{align*} & \mathrm{IF}{\quad}z_{1}(t)\,\text{is}\,N_{i1}\,\text{and}\ldots z_{p}(t)\,\text{is}\,N_{ip}\\ & \mathrm{THEN}{\quad}\begin{bmatrix}\dot{x}\\ z\end{bmatrix}=\begin{bmatrix}A_{i} & B_{1i} & B_{2i}\\ C_{i} & D_{11i} & D_{12i}\end{bmatrix}\begin{bmatrix}x\\ w\\ u\end{bmatrix}.\tag{1} \end{align*}$$