• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.61 no.10
• /
• pp.1508-1512
• /
• 2012

This paper presents a relaxed stability condition for continuous-time affine fuzzy system using fuzzy Lyapunov function. In the previous studies, stability conditions for the affine fuzzy system based on quadratic Lyapunov function have a conservativeness. The stability condition is considered by using the fuzzy Lyapunov function, which has membership functions in the traditional Lyapunov function. Based on Lyapunov-stability theory, the stability condition for affine fuzzy system is derived and represented to linear matrix inequalities(LMIs). And slack matrix is added to stability condition for the relaxed stability condition. Finally, simulation example is given to illustrate the merits of the proposed method.

• Journal of the Korean Data and Information Science Society
• /
• v.12 no.1
• /
• pp.89-97
• /
• 2001

Chen and Chen(FSS, 1993, 159-168) presented a reasonable analytical model of fuzzy closed-loop systems and proposed a method to analyze the stability of fuzzy control by the relational matrix of fuzzy system. Chen, Lu and Chen(IEEE Trans. Syst. Man Cybern., 1995, 881-888) formulated the sufficient and necessary conditions on stability of fuzzy closed-loop control systems. Gang and Chen(FSS, 1996, 27-34) deduced a linguistic relation model of a fuzzy closed loop control system from the linguistic models of the fuzzy controller and the controlled process and discussed the linguistic stability of fuzzy closed loop system by a linguistic relation matrix. In this paper, we study more on their models. Indeed, we prove the existence and uniqueness of equilibrium state $X_e$ in which fuzzy system is stable and give closed form of $X_e$. The same examples in Chen and Chen and Gang and Chen are treated to analyze the stability of fuzzy control systems.

• Journal of Advanced Marine Engineering and Technology
• /
• v.28 no.8
• /
• pp.1299-1312
• /
• 2004

This paper suggests the simple form of a fuzzy PID controller and describes the design principle, tracking performance, stability analysis and changes of parameters of a suggested fuzzy PID controller. A fuzzy PID controller is derived from the design procedure of fuzzy control. It is well known that a fuzzy PID controller has a simple structure of the conventional PID controller but posses its self-tuning control capability and the gains of a fuzzy PID controller become nonlinear functions of the inputs. Nonlinear calculation during fuzzification, defuzzification and the fuzzy inference require more time in computation. To increase the applicability of a fuzzy PID controller to digital computer, a simple form of a fuzzy PID controller is introduced by the backward difference mapping and the analysis of the fuzzy input space. To guarantee the BIBO stability of a suggested fuzzy PID controller, ‘small gain theorem’ which proves the BIBO stability of a fuzzy PI and a fuzzy PD controller is used. After a detailed stability analysis using ‘small gain theorem’, from which a simple and practical method to decide the parameters of a fuzzy PID controller is derived. Through the computer simulations for the linear and nonlinear plants, the performance of a suggested fuzzy PID controller will be assured and the variation of the gains of a fuzzy PID controller will be investigated.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.3
• /
• pp.563-570
• /
• 2010

In this article, we take account of the fuzzy stability for generalized derivation in fuzzy Banach algebra.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.11 no.7
• /
• pp.574-578
• /
• 2001

The stability analysis for the fuzzy logic controller (FLC) has widely been reported. Furthermore many research in the FLC has been introduced to decrease the number of parameters representing the antecedent part of the fuzzy control rule. In this paper we briefly explain a single-input fuzzy logic controller (SFLC) or simple-structured FLC which uses only a single input variable. And then we analyze that it is absolutely stale based on the sector bounded condition. We also show the feasibility of the proposed stability analysis through a numerical example of a mass-damper-spring system.

• Journal of Advanced Marine Engineering and Technology
• /
• v.20 no.2
• /
• pp.101-101
• /
• 1996

This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptaion controllers which guarantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

• Journal of Advanced Marine Engineering and Technology
• /
• v.20 no.2
• /
• pp.33-39
• /
• 1996

This paper presents the linearized fuzzy modeling technique of nonlinear dynamical system and the stability analysis of fuzzy control system. Firstly, the nonlinear system is partitionized by multiple linear fuzzy subcontrol systems based on fuzzy linguistic variables and fuzzy rules. Secondly, the disturbance adaptaion controllers which guarantee the global asymptotic stability of each fuzzy subsystem by an optimal feedback control law are designed and the stability analysis procedures of the total fuzzy control system using Lyapunov functions and eigenvalues are discussed in detail through a given illustrative example.

• 제어로봇시스템학회:학술대회논문집
• /
• 1998.10a
• /
• pp.265-270
• /
• 1998

In this paper we introduce a modeling of wheeled mobile robot with a differential drive derived by R.M. DeSantis and using the dynamics model-ing with some disturbance term we control the wheeled mobile robot using fuzzy sliding mode control(FSMC) method. In a fuzzy control approach it is very difficult to prove the stability of the fuzzy controller. Therefore, to overcome that difficult proof of the stability in a fuzzy control method, we first propose a sliding mode controller and prove the stability of the proposed controller. Next, transforming the proposed sliding mode controller into a fuzzy sliding mode controller without changing the basic structure of the sliding mode con-troller, we easily obtain a fuzzy sliding mode con-troller(FSMC) whose stability is guaranteed with-out difficult stability proof procedure of the proposed FSMC.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1993.06a
• /
• pp.1090-1093
• /
• 1993

In this paper, the design technique of fuzzy controller using pole placement method and the stability analysis of the system are discussed. The consequent parts of the fuzzy model representing the fuzzy control system are descrived by linear stated equations. It cannot be guaranteed that the total fuzzy system is stable even if all subsystems are stable. The range of the consequent parameters of fuzzy feedback controller which is stable for each fuzzy subspace of the input space are derived, using a rather simplified stability criterion. Then, the consequent parameters of fuzzy controller is determined with the sufficient condition that the fuzzy feedback controller maintain robust stability for the model of other subspace.

• Korean Journal of Mathematics
• /
• v.22 no.4
• /
• pp.659-670
• /
• 2014

In this paper, we prove the Hyers-Ulam stability of homomorphisms in fuzzy Banach algebras and of derivations on fuzzy Banach algebras associated to the Cauchy-Jensen functional equation.