A New Control Law for TS Fuzzy Models: Less Conservative LMI Conditions by Using Membership Functions Derivative

TL;DR

This paper introduces a novel control law for TS fuzzy models that reduces conservativeness by incorporating membership function derivatives into the control design, formulated via LMIs.

Contribution

It proposes a new Parallel Distributed Controller for TS fuzzy models that includes membership function derivatives, improving control performance over traditional methods.

Findings

The new control law is less conservative than traditional PDC.

Design conditions are expressed as LMIs solvable with numerical tools.

Numerical examples demonstrate the advantages of the proposed approach.

Abstract

This note proposes a new type of Parallel Distributed Controller (PDC) for Takagi-Sugeno (TS) fuzzy models. Our idea consists of using two control terms based on state feedback, one composed of a convex combination of linear gains weighted by the normalized membership grade, as in traditional PDC, and the other composed of linear gains weighted by the time-derivatives of the membership functions. We present the design conditions as Linear Matrix Inequalities, solvable through numerical optimization tools. Numerical examples are given to illustrate the advantages of the proposed approach, which contains the the traditional PDC as a special case.