SOS-based fuzzy stability analysis via homogeneous Lyapunov functions

Lo, Ji Chang; Lin, Yezhe; Chang, Wei; Lin, Fong Yi

doi:10.1109/fuzz-ieee.2014.6891652

Cited by 11 publications

(6 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, using P(x(t)) has potential to relax the stability analysis as more state information is utilized. Two-step approach [147], solution search method [87], homogeneous polynomial form of Lyapunov function [148] and elimination technique by setting equality constraints [149] were proposed in the stability analysis using P(x(t)) as the polynomial Lyapunov function candidate.…”

Section: Dtmentioning

confidence: 99%

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

Lam

2018

Engineering Applications of Artificial Intelligence

227

111

View full text Add to dashboard Cite

show abstract

Section: Dtmentioning

confidence: 99%

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

Lam

2018

Engineering Applications of Artificial Intelligence

227

111

View full text Add to dashboard Cite

show abstract

“…In a new approach and without compromising the globality of stability analysis, the HPLF has been applied to polynomial systems by defining Euler's homogeneity relationship [28]. Then, by emerging the Polynomial Fuzzy Systems (PFS), the HPLF was applied to the state feedback stabilization problem [29]. The application of HPLF avoids non-convex terms and limitations on defining the Lyapunov function.…”

Section: Introductionmentioning

confidence: 99%

“…Later on, to reduce the effect of the non-convex factor (created by the polynomial Lyapunov function differentiation), an optimization operation along with stability condition realization was proposed for the FTC problems [21]. Eventually, the application of the homogeneous polynomial Lyapunov function (HPLF) was proposed to eliminate the mentioned restrictions [15,[28][29][30]. The homogeneity characteristic of the Lyapunov function avoids the implicit creation of the Lyapunov matrix derivative in stability analysis.…”

Section: Introductionmentioning

confidence: 99%

Robust fuzzy observer‐based fault‐tolerant control: A homogeneous polynomial Lyapunov function approach

Sabbaghian-Bidgoli

Farrokhi

2022

IET Control Theory & Appl

View full text Add to dashboard Cite

In this paper, a homogeneous polynomial Lyapunov function (HPLF) is employed in robust observer‐based Integrated Fault‐Tolerant Control (IFTC) of nonlinear systems modelled by the polynomial fuzzy model (PFM). This makes the design problem benefit from the conservative reduction property of polynomial Lyapunov functions (PLFs) and simultaneously avoid the emergence of non‐convex terms due to differentiation of the polynomial Lyapunov matrix. As a result, the less conservative sum of square (SOS) conditions are obtained in the form of polynomial matrix inequalities (PMI), which are solved via SOSTOOLS. For the first time, a non‐quadratic Lyapunov function is used to design a polynomial fuzzy unknown‐input observer that estimates the system's states and actuator faults in the presence of model uncertainties and external disturbances. The effectiveness of the proposed approach in providing more relaxed and less conservative results along with the better fault tolerance is illustrated through three simulating examples and compared with the quadratic Lyapunov function (QLF) approach.

show abstract

“…The SOS-based stability/stabilization conditions were thus derived in many studies [7], [8] to ensure the stability of T-S fuzzy polynomial system and facilitate the controller synthesis. In addition, some SOS-based relaxed stability/stabilization conditions are proposed in [9]- [11].…”

Section: Introductionmentioning

confidence: 99%

A novel stabilization condition for T-S polynomial fuzzy system with time-delay: A sum-of-squares approach

Tsai

Chen

et al. 2016

2016 IEEE International Conference on Systems, Man, and Cybernetics (SMC)

Self Cite

View full text Add to dashboard Cite

, H-K. (2017). A novel stabilization condition for T-S polynomial fuzzy system with time-delay: A sum-of-squares approach. In 2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016 -Conference Proceedings (pp. 1555-1560 General rightsCopyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights.•Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research.•You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact librarypure@kcl.ac.uk providing details, and we will remove access to the work immediately and investigate your claim. Abstract-A novel stabilization problem for T-S polynomial fuzzy system with time-delay is investigated in this paper. Firstly, a polynomial fuzzy controller for T-S polynomial fuzzy system with time-delay is proposed. In addition, based on polynomial Lyapunov-Krasovskii function and the developed polynomial slack variable matrices, a novel stabilization condition for T-S polynomial fuzzy system with time-delay is presented in terms of sum-of-square (SOS) form. Lastly, nonlinear system with timedelay and a well-known T-S fuzzy system with time-delay are illustrated to demonstrate the feasibility and effectiveness of the proposed results.

show abstract

SOS-based fuzzy stability analysis via homogeneous Lyapunov functions

Cited by 11 publications

References 15 publications

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

A review on stability analysis of continuous-time fuzzy-model-based control systems: From membership-function-independent to membership-function-dependent analysis

Robust fuzzy observer‐based fault‐tolerant control: A homogeneous polynomial Lyapunov function approach

A novel stabilization condition for T-S polynomial fuzzy system with time-delay: A sum-of-squares approach

Contact Info

Product

Resources

About