Polynomial fuzzy-model-based control systems: Stability analysis via RHS copositive relaxation

Author

Ji-Chang Lo ; Feng-Yi Lin ; Ge-Chang Yang

Author_Institution

Mech. Eng., Nat. Central Univ., Jhongli, Taiwan

fYear

2013

fDate

7-10 July 2013

Firstpage

1

Lastpage

8

Abstract

Based on recent results on homogeneous polynomially parameter-dependent (HPPD) solutions to parameter-dependent LMIs (PD-LMIs), we investigate, via right-hand side (RHS) relaxations, the stability analysis of polynomial fuzzy-model-based control systems. The PFMB control system under consideration requires that the polynomial fuzzy model and controller share (1) perfect match or (2) un-perfect match of premise membership functions. This paper proposes a new SOS condition via RHS relaxation and reduces the conservatism of existing PD-LMI results. To verify the analytical theories regarding PFMB stability, two examples are demonstrated to show the effectiveness of the proposed approach.

Keywords

fuzzy control; linear matrix inequalities; polynomials; relaxation theory; stability; HPPD solutions; PD-LMIs; PFMB control system; RHS copositive relaxation; RHS relaxations; homogeneous polynomially parameter-dependent solutions; membership functions; parameter-dependent LMIs; polynomial fuzzy-model-based control systems; right-hand side relaxations; stability analysis; sum of squares condition; Asymptotic stability; Control systems; Polynomials; Stability analysis; Symmetric matrices; Thermal stability; Vectors; Parameter-Dependent Linear Matrix Inequality (PD-LMI); Polynomial TS Fuzzy Models; Right-Hand Side (RHS) Relaxations; Sum Of Squares (SOS);

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems (FUZZ), 2013 IEEE International Conference on

Conference_Location

Hyderabad

ISSN

1098-7584

Print_ISBN

978-1-4799-0020-6

Type

conf

DOI

10.1109/FUZZ-IEEE.2013.6622353

Filename

6622353