• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1993.06a
• /
• pp.953-955
• /
• 1993

In this paper we propose a new stability theorem and a robust stability condition for linguistic fuzzy model systems in state space. First we define a stability in linear sense. After representing the fuzzy model by a system with disturbances, A necessary and sufficient condition for the stability is derived. This condition is proved to be a sufficient condition of the fuzzy model. The Q in the Lyapunov equation is iteratively adjusted by an gradient-based algorithm to improve its stability test. Finally, stability robustness bounds of a system having modeling error is derived. An example is also included to show that the stability test is powerful.

• Proceedings of the KIEE Conference
• /
• 2001.11c
• /
• pp.76-79
• /
• 2001

This paper is concerned with a stability analysis of Madam Type fuzzy systems. It Introduces the canonical form of an unforced fuzzy system and its stability theorem suggested in the previous study. Then it gives new simplified stability conditions based on the Lyapunov function method. A common positive definite matrix in the stability conditions is searched by the LMI method.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.2 no.1
• /
• pp.78-82
• /
• 2002

In this paper, we have studied a numerical stability analysis method for the robust fuzzy feedback linearization regulator using Takagi-Sugeno fuzzy model. To analyze the robust stability, we assume that uncertainty is included in the model structure with known bounds. For these structured uncertainty, the robust stability of the closed system is analyzed by applying Linear Matrix Inequalities theory following a transformation of the closed loop systems into Lur'e systems.

• 제어로봇시스템학회:학술대회논문집
• /
• 1999.10a
• /
• pp.169-172
• /
• 1999

In this paper, piecewise quadratic Lyapunov functions are used to analyze the stability of fuzzy-model-based controller. We represent the nonlinear system using a Takagi-Sugeno fuzzy model, which represent the given nonlinear system by fuzzy inference rules and local linear dynamic models. The proposed stability analysis technique is developed by dividing the whole fuzzy system into the smaller separate fuzry systems to reduce the conservatism. Some necessary and sufficient conditions for the proposed method are obtained. Finally, stability of the closed system with various kinds of controller for TS fuzzy model is checked through the proposed method.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.05a
• /
• pp.47-51
• /
• 2001

According as the controlled plants become more complex and large-scaled, the development of more intelligent control schemes is required in the control field. A fuzzy logic control (FLC) is one of proper schemes for this tendency. Recently, fuzzy control has been applied successfully to many industrial applications due to a number of advantages. But it still has some disadvantages. The conventional FLC has many tuning parameters: membership functions, scaling factors, and so forth. In order to improve this problem, a single-input fuzzy logic control (SFIC) which greatly simplifies the design process of the conventional FLC was proposed. Many research has also been proposed to develop the stability analysis of the FLC. In this paper we analyze the absolute stability of the SFLC. We first expand a nonlinear controlled plant into a Taylor series about a nominal operating point. And a fuzzy control system is transformed into a Lure system with nonlinearities. We also prove that the closed-loop system with the SFLC satisfies the sector condition globally.

• Smart Structures and Systems
• /
• v.31 no.1
• /
• pp.69-78
• /
• 2023

The purpose of this paper is to develop a scalable grey predictive controller with unavoidable random delays. Grey prediction is proposed to solve problems caused by incorrect parameter selection and to eliminate the effects of dynamic coupling between degrees of freedom (DOFs) in nonlinear systems. To address the stability problem, this study develops an improved gray-predictive adaptive fuzzy controller, which can not only solve the implementation problem by determining the stability of the system, but also apply the Linear Matrix Inequality (LMI) law to calculate Fuzzy change parameters. Fuzzy logic controllers manipulate robotic systems to improve their control performance. The stability is proved using Lyapunov stability theorem. In this article, the authors compare different controllers and the proposed predictive controller can significantly reduce the vibration of offshore platforms while keeping the required control force within an ideal small range. This paper presents a robust fuzzy control design that uses a model-based approach to overcome the effects of modeling errors. To guarantee the asymptotic stability of large nonlinear systems with multiple lags, the stability criterion is derived from the direct Lyapunov method. Based on this criterion and a distributed control system, a set of model-based fuzzy controllers is synthesized to stabilize large-scale nonlinear systems with multiple delays.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.8 no.4
• /
• pp.53-61
• /
• 1998

This paper describes the stability analysis of TSK (Takagi-Sugeno-Kang) fuzzy systems which can represent a large class of nonlinear systems with good accuracy. A TSK fuzzy model consists of TSK fuzzy rules and the consequent of each fuzzy rule is a linear input-output equation with a constant term. There may exist equilibrium points more than one in the TSK fuzzy model and each equilibrium point rnay also have different nature of stability. The local stability of an equilibrium point is determined by eigenvalues of the Jacobian matrix of the linearized TSK fuzzy model around the equilibrium point. Stability of both the continuous-time and the discrete-time systems is analyzed in this paper.

• Proceedings of the IEEK Conference
• /
• 2001.06c
• /
• pp.169-172
• /
• 2001

In recent years, many studies regarding the modeling of fuzzy system have been conducted. In this paper, a new computational approach to modeling of linguistic fuzzy system is proposed The fuzzy system is modeled as a combination of affine systems, The proposed method can be used in a rigorous stability analysis of fuzzy system including the linguistic fuzzy controller.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.40 no.4
• /
• pp.235-242
• /
• 2003

In this paper, a fuzzy controller is designed to suppress and stabilize the chaotic behavior of Chua's circuit. This controller is constructed by the following two phases. First, Chua's circuit is represented by an affine fuzzy model. Second, a fuzzy controller is designed so that the stability of the closed-loop system composed of the fuzzy controller and the affine fuzzy model of Chua's circuit is rigorously guaranteed. The stability condition of the affine fuzzy system is derived and is recast in the formulation of linear matrix inequalities. The guaranteed stability is global and asymptotic. Finally, the applicability of the suggested methodology is highlighted via computer simulations.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.1
• /
• pp.123-132
• /
• 2014

In this paper, we investigate the following form of a certain class of quadratic functional equations and its fuzzy stability. $$f(kx+y)+f(kx-y)=f(x+y)+f(x-y)-2(1-k^2)f(x)$$ where k is a fixed rational number with $k{\neq}1$, -1, 0.