Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

Authors:
Miguel Bernal;Antonio Sala;Abdelhafidh Jaadari;Thierry-Marie Guerra
Affiliations:
Department of Electric & Electronics Engineering at the Sonora Institute of Technology, Mexico;Instituto de Automática e Informática Industrial (AI2), Universitat Politecnica de Valencia, Spain;LAMIH FRE CNRS 3304, University of Valenciennes and Hainaut-Cambrésis, France;LAMIH FRE CNRS 3304, University of Valenciennes and Hainaut-Cambrésis, France
Venue:
Fuzzy Sets and Systems
Year:
2011

Citing 17
Cited 1

Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach

Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach
Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem

Fuzzy Sets and Systems
Relaxed LMI conditions for closed-loop fuzzy systems with tensor-product structure

Engineering Applications of Artificial Intelligence
A membership-function-dependent approach for stability analysis and controller synthesis of Takagi--Sugeno models

Fuzzy Sets and Systems
Guaranteed cost control of polynomial fuzzy systems via a sum of squares approach

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems

IEEE Transactions on Fuzzy Systems
Perspectives of fuzzy systems and control

Fuzzy Sets and Systems
A way to escape from the quadratic framework

FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
Polynomial fuzzy models for nonlinear control: a Taylor series approach

IEEE Transactions on Fuzzy Systems
Generalized nonquadratic stability of continuous-time Takagi-Sugeno models

IEEE Transactions on Fuzzy Systems
An approach to fuzzy control of nonlinear systems: stability and design issues

IEEE Transactions on Fuzzy Systems
Piecewise quadratic stability of fuzzy systems

IEEE Transactions on Fuzzy Systems
Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems

IEEE Transactions on Fuzzy Systems
A multiple Lyapunov function approach to stabilization of fuzzy control systems

IEEE Transactions on Fuzzy Systems
Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions

IEEE Transactions on Fuzzy Systems
Relaxed Stability and Performance LMI Conditions for Takagi--Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes

IEEE Transactions on Fuzzy Systems
LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form

Automatica (Journal of IFAC)

Local stability analysis of continuous-time Takagi-Sugeno fuzzy systems: A fuzzy Lyapunov function approach

Information Sciences: an International Journal

Quantified Score

Hi-index	0.20

Visualization

Abstract

In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinement of the polynomial Lyapunov function so as to make it share the fuzzy structure of the model proves advantageous. Conditions thus obtained are tested via available SOS software.