Multiple Models Approach in Automation: Takagi-Sugeno Fuzzy Systems

Chapter 5

Robust Stabilization of Multiple Models

5.1. Introduction

This chapter is essentially devoted to the synthesis of robust control laws for uncertain multiple models. We consider two types of uncertainties: structural norm-bounded and interval uncertainties. Sufficient conditions for the stabilization of uncertain multiple models based on the existence of quadratic Lyapunov functions are proposed. The aim is to present synthesis methods for state–space feedback control, static output feedback and observer-based control laws [CHA 06a, CHA 07]. These synthesis conditions are expressed in an LMI form.

The uncertain multiple model considered is as follows:

[5.1]

where is the number of local models, is the state vector, is the control vector, is the output vector, and are the ith state, ...