Asymptotically necessary and sufficient stability conditions for discrete-time Takagi-Sugeno model: extended applications of Polya's theorem and homogeneous polynomials

DOI10.1016/j.jfranklin.2013.09.025zbMath1293.93648OpenAlexW1968865345MaRDI QIDQ398473

Tao Zou, Hai-Bin Yu

Publication date: 15 August 2014

Published in: Journal of the Franklin Institute (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfranklin.2013.09.025

zbMATH Keywords

asymptotically necessary and sufficient (ANS) stabilit homogeneously polynomially nonquadratic (HPNQ) Lyapunov functionsdiscrete-time Takagi-Sugeno modelhomogeneously polynomially parameterized (HPP) state feedback lawsnecessary and sufficient stability conditionsPólya's theorem: asymptotically necessary and sufficient (ANS) stability and stabilization

Mathematics Subject Classification ID

Fuzzy control/observation systems (93C42) Discrete-time control/observation systems (93C55) Asymptotic stability in control theory (93D20)

Related Items (8)

Improvement on stability conditions for continuous-time T-S fuzzy systems ⋮ Co-design of event-triggered \(H_\infty\) control for discrete-time linear parameter-varying systems with network-induced delays ⋮ Observer design of discrete-time T-S fuzzy systems via multi-instant augmented multi-indexed matrix approach ⋮ Further studies on stability and stabilization conditions for discrete-time T-S systems with the order relation information of membership functions ⋮ A multiple-parameterization approach for local stabilization of constrained Takagi-Sugeno fuzzy systems with nonlinear consequents ⋮ Novel stability conditions for discrete-time T-S fuzzy systems: a Kronecker-product approach ⋮ New relaxed stability and stabilization conditions for continuous-time T-S fuzzy models ⋮ Asymptotically necessary and sufficient conditions for Takagi-sugeno models using generalized non-quadratic parameter-dependent controller design

Uses Software

• Matlab
• LMI toolbox

Cites Work

• Stability analysis and design of fuzzy control systems
• Analysis and design for a class of complex control systems. II: Fuzzy controller design
• New approaches to \(H_{\infty}\) controller designs based on fuzzy observers for T-S fuzzy systems via LMI
• LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form
• Stabilization via extended nonquadratic boundedness for constrained nonlinear systems in Takagi-Sugeno's form
• Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: applications of Polya's theorem
• Improvement on observer-based \(H_{\infty}\) control for T--S fuzzy systems
• Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form
• Reformulation of LMI-based stabilisation conditions for non-linear systems in Takagi–Sugeno's form
• New results on robust H _∞ filtering design for discrete-time piecewise linear delay systems
• Fuzzy identification of systems and its applications to modeling and control
• Parameter-Dependent LMIs in Robust Analysis: Characterization of Homogeneous Polynomially Parameter-Dependent Solutions Via LMI Relaxations
• Control laws for Takagi-Sugeno fuzzy models
• Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties

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