Details

Title

Stabilization of a certain class of fuzzy control systems with uncertainties

Journal title

Archives of Control Sciences

Yearbook

2017

Numer

No 3

Publication authors

Divisions of PAS

Nauki Techniczne

Description

Archives of Control Sciences welcomes for consideration papers on topics of significance in broadly understood control science and related areas, including: basic control theory, optimal control, optimization methods, control of complex systems, mathematical modeling of dynamic and control systems, expert and decision support systems and diverse methods of knowledge modelling and representing uncertainty (by stochastic, set-valued, fuzzy or rough set methods, etc.), robotics and flexible manufacturing systems. Related areas that are covered include information technology, parallel and distributed computations, neural networks and mathematical biomedicine, mathematical economics, applied game theory, financial engineering, business informatics and other similar fields.

Aims and Scope: Archives of Control Sciences publishes papers in the broadly understood field of control science and related areas while promoting the closer integration of the Polish, as well as other Central and East European scientific communities with the international world of science.

Abstract

Abstract In this paper, we investigate the global uniform practical exponential stability for a class of uncertain Takagi-Sugeno fuzzy systems. The uncertainties are supposed uniformly to be bounded by some known integrable functions to obtain an exponential convergence toward a neighborhood of the origin. Therefore, we use common quadratic Lyapunov function (CQLF) and parallel distributed compensation (PDC) controller techniques to show the global uniform practical exponential stability of the closed-loop system. Numeric simulations are given to validate the proposed approach.

Publisher

Committee of Automatic Control and Robotics PAS

Date

2017

Identifier

ISSN 1230-2384

References

ZHANG (2001), Stability analysis and systtematic design of fuzzy control systems Fuzzy Sets Systems, null, 31, 120. ; LIU (2003), New approach to controller designs based on fuzzy observers for fuzzy systems via, Automatica, 15, 39. ; JIANG (1998), Design of robust adaptive controllers for nonlinear systems with dynamic uncertainties, Automatica, 33, 825. ; CORLESS (1981), LEITMANN Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems on Automatic Control, IEEE Trans, 16, 1139. ; BASSEM BEN HAMED (2010), Practical uniform stability of nonlinear differential delay equations of, Mathematics, 139. ; LAKSHMIKANTHAM (1990), Practical Stability of Nonlinear Systems World Scientific Singapore, null, 12. ; TANG (2001), modified fuzzy PI controller for a flexible - joint robot arm with uncertainties Fuzzy Sets Systems, null, 28, 109. ; Sugeno (1988), Structure identification of fuzzy model Fuzzy Sets Systems, null, 20, 15. ; TAKAGI (1985), Fuzzy identification of systems and its applications to modeling and control on Systems Part, IEEE Trans Man Cybernetics Cybernetics, 22, 116. ; CAO (1996), Stability analysis and design for class of continuous - time fuzzy control systems of Control, Int J, 1069. ; CORLESS (1990), Guaranteed rates of exponential convergence for uncertain systems of Optimization Applications, Theory, 17, 481. ; XIAO (2011), Relaxed results on stabilization and state feedback control conditions for fuzzy systems of Innovative and, Int J Computing Information Control, 24, 1753. ; ZADEH (1973), Outline of a new approach to the analysis of complex systems and decision process on Systems Part, IEEE Trans Man Cybernetics Cybernetics, 30, 28. ; LINNA ZHOU (2006), Practical stability analysis and synthesis of a class of uncertain fuzzy systems Fuzzy Systems and Knowledge Discovery in, Lecture Notes Computer Science, 14, 4223. ; TAI (2008), ZU Design of variable structure control for fuzzy nonlinear systems Expert System with Applications, null, 21, 1496. ; WU (2006), Stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function of Control, Int J, 1635. ; Corless (1993), Leitmann Bounded controllers for robust exponential convergence of Optimization Applications, Theory, 18, 1. ; Bassem Ben Hamed (2009), Practical stabilisation of a class of uncertain time - varying nonlinear delay systems of Control Theory and Applications, null, 175. ; WANG (1995), Parallel distributed compensation of nonlinear systems by model Proceedings of Fuzzy, null, 26, 95. ; BENZAOUIA (2011), Delay - dependent stabilization conditions of controlled positive fuzzy systems with time varying delay of Innovative and, Int J Computing Information Control, 1. ; FENG (1997), Design of fuzzy control systems with guaranteed stability Fuzzy Sets Systems, null, 85. ; TAIEB (2012), HADJ On the global stabilization of fuzzy cascaded systems, Nonlinear Dynamics, 19, 67. ; XIAOJIE SU (null), novel approach to filter design for fuzzy discrete - time systems with time - varying delay to appear in IEEE Transactions Fuzzy Systems, null, 25. ; WANG (1996), An approach to fuzzy control of nonlinear systems : Stability and design issues Fuzzy Systems, IEEE Trans, 27. ; LIGANG WU (2011), Model approximation for discrete - time state - delay systems in the fuzzy framework Fuzzy Systems, IEEE Trans, 11, 366. ; BEN ABDALLAH (2009), Practical stability of nonlinear time - varying cascade systems of Dynamical and Control Systems, null, 15, 45. ; SOLDATOS (1991), Stabilizing uncertain systems with bounded control and, Dynamics Control, 1. ; CHANG (2011), WEN Robust fuzzy control via observer feedback for passive stochastic fuzzy systems with time - delay and multiplicative noise of Innovative and, Int J Computing Information Control, 29, 345. ; LASALLE (1961), Stability by Lyapunov s Direct Method with Application Academic Press New York, null, 13. ; TANAKA (1996), Robust stabilization of a class of uncertain nonlinear systems via fuzzy control : quadratic stabilizability control theory and linear matrix inequalities Fuzzy Systems, IEEE Trans, 1. ; TONG (1977), control engineering review of fuzzy systems, Automatica, 23, 559.

DOI

10.1515/acsc-2017-0028

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