Multiple Models Approach in Automation: Takagi-Sugeno Fuzzy Systems

Chapter 4

Stabilization of Multiple Models

4.1. Introduction

The previous chapters have been devoted to analyzing the stability of multiple models and state estimation, based on Lyapunov functions and LMI formulation. In this chapter, we discuss some control law synthesis approaches.

The synthesis of controllers has been actively considered in recent years and numerous studies have been published in this area. These studies, which have been mostly inspired by control techniques found in literature, have dealt with control through static and dynamic full state feedback, with and without uncertainties [CHA 10, CHA 06b, GUE 04, JAD 99, JOH 98, KRU 08, TAN 01, TAN 98]. Multiobjective synthesis techniques have also been tackled.

4.2. Full state feedback control

The continuous closed-loop multiple model via PDC control law [2.40] is given by:

[4.1]

Synthesis of control laws using full state feedback can be obtained by directly replacing the analysis conditions, state matrices for open-loop multiple models with those relating to closed-loop multiple models, i.e.:

The obtained result has the drawback of being very conservative and not directly formulated as an LMI problem. However, as has already been described, there are multiple methods for reducing it to an LMI problem. Some relaxation techniques ...