• International Journal of Control, Automation, and Systems
• /
• 제4권4호
• /
• pp.448-455
• /
• 2006

This paper deals with the observer design problem for a class of state-delayed nonlinear systems with or without time-varying norm-bounded parameter uncertainty. The nonlinearities under consideration are assumed to satisfy the global Lipschitz conditions and appear in both the state and measured output equations. The problem we address is the design of a nonlinear observer such that the resulting error system is globally asymptotically stable. For the case when there is no parameter uncertainty, a sufficient condition for the solvability of this problem is derived in terms of linear matrix inequalities and the explicit formula of a desired observer is given. Based on this, the robust observer design problem for the case when parameter uncertainties appear is considered and the solvability condition is also given. Both of the solvability conditions obtained in this paper are delay-dependent. A numerical example is provided to demonstrate the applicability of the proposed approach.

• International Journal of Control, Automation, and Systems
• /
• 제6권1호
• /
• pp.24-34
• /
• 2008

A novel neural network model, termed the standard neural network model (SNNM), similar to the nominal model in linear robust control theory, is suggested to facilitate the synthesis of controllers for delayed (or non-delayed) nonlinear systems composed of neural networks. The model is composed of a linear dynamic system and a bounded static delayed (or non-delayed) nonlinear operator. Based on the global asymptotic stability analysis of SNNMs, Static state-feedback controller and dynamic output feedback controller are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based nonlinear systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Two application examples are given where the SNNMs are employed to synthesize the feedback stabilizing controllers for an SISO nonlinear system modeled by the neural network, and for a chaotic neural network, respectively. Through these examples, it is demonstrated that the SNNM not only makes controller synthesis of neural-network-based systems much easier, but also provides a new approach to the synthesis of the controllers for the other type of nonlinear systems.

• 전자공학회논문지SC
• /
• 제49권2호
• /
• pp.17-25
• /
• 2012

본 논문에서는 입력에 시간지연이 있는 연속 비선형 시스템의 일반적인 이산화를 위해 높은 차수의 샘플링 보관법을 제안한다. 제안한 방법은 테일러 시리즈 확장, 샘플링 이론과 보관법의 조합을 기초로 한다. 새로운 이산화 방법의 수학적인 구조에 대해 세부적으로 유도하였으며, 제안한 이산화 방법에 대한 성능을 2차 시스템에 대한 시뮬레이션을 통해 검증하였다.

• 전기학회논문지
• /
• 제61권3호
• /
• pp.459-465
• /
• 2012

In this paper, we present a non-fragile guaranteed cost control design method for uncertain nonlinear systems with time varying delays in state and control input, even though the controller gain is perturbed. The uncertain nonlinear term in the systems is norm bounded and the linear matrix inequality(LMI) optimization method is employed as a stability analysis of the systems. We design a robust controller and show the asymptotical stability of uncertain time-varying systems based on Lyapunov method. Also, we guarantee a specific level of performance of the systems. The simulations are carried out to demonstrate the effectiveness of the proposed method.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 1998년도 하계종합학술대회논문집
• /
• pp.227-230
• /
• 1998

In this paper, we propose the design method of fuzzy robust H$\infty$ controller for the uncertain nonlinear discete-time systems with time delay. First, we represent a nonlinear plant with a modified T-S(Takagi-Sugeno) fuzzy model. Then design method utilizing the concept of PDC (parallel distributed compensation) is employed. For the modified T-S fuzzy model with uncertainty and delay, the sufficient condition of the quadratic stabilization with an H$\infty$ norm bound is presented in terms of Lyapunov stability theory and fuzzy robust H$\infty$ controller design method is given by LMI(linear matrix inequality) approach. Also an illustrative example is given to demonstrate the result of the proposed method.

• 한국지능시스템학회논문지
• /
• 제19권6호
• /
• pp.779-786
• /
• 2009

본 논문에서는 시간지연을 가지는 이산 비선형 마코비안 점프 시스템의 $H_{\infty}$ 퍼지 제어 문제를 다룬다. Takgi-Sugeno 퍼지 모델을 이용하여 마코비안 점프 파라미터를 갖는 시간 지연 비선형 시스템을 마코비안 점프 퍼지 시스템으로 나타내고, 이에 대한 제어기를 설계한다. 확률 퍼지-리아프노프(Lyapunov) 함수를 이용하여 안정성 및 $H_{\infty}$ 성능을 해석하고 이 함수를 이용하여 폐루프 시스템이 안정하며 $H_{\infty}$ 성능 조건을 만족하는 조건식을 유도한다. 확률 퍼지-리아프노프 함수는 시스템 모드에 따라 변하는 함수이다. 유도된 조건식으로부터 제어기 존재 조건을 선형행렬부등식으로 나타내며, 제어기는 선형행렬부등식으로부터 바로 구할 수 있다. 수치적 예제 및 컴퓨터 시뮬레이션을 통하여 제안된 방법의 타당성을 보인다.

• 한국정밀공학회지
• /
• 제14권4호
• /
• pp.88-96
• /
• 1997

This paper suggests a new non-linear friction compensation for digital control systems. This control adopts a hysteresis nonlinear element which can introduce the phase lead of the control system to compensate the phase delay comes from the inherent time delay of a digital control. A proper Lyapunov function is selected and the Lyapunov direct method is used to prove the asymptotic stability of the suggested control.

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 1996년도 추계학술대회 논문집
• /
• pp.987-993
• /
• 1996

This report suggests a new non-linear friction compensation for digital control systems. This control adopts a hysteric nonlinear clement which can introduce the phase lead of the control system to compensate the phase delay comes from the inherent time delay of a digital control. The Lyapunov direct method is used to prove the asymtotic stability of the suggested control, and the stability and the effectiveness are verified analytically and experimentally on a single axis servo driving system.

• 제어로봇시스템학회논문지
• /
• 제2권3호
• /
• pp.158-164
• /
• 1996

In this paper, we consider the problem of robust stability of discretd time-delay systems subjected to perturbations. Two classes of perturbations are treated. The first one is the nonlinear norm-bounded perturbation, and the second is the structured time-varying parametric perturbation. Based on the discrete-time Lyapunov stability theory, several new sufficient conditions for robust stability of the system are presented. From these conditions, we can estimate the maximum allowable bounds of the perturbations which guarantee the stability. Finally, numerical examples are given to demonstrate the effectiveness of the results.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제8권2호
• /
• pp.151-157
• /
• 2008

A non-fragile guaranteed cost control (GCC) problem is presented for a class of discrete time-delay nonlinear systems described by Takagi-Sugeno (T-S) fuzzy model. The systems are assumed to have norm-bounded time-varying uncertainties in the matrices of state, delayed state and control gains. Sufficient conditions are first obtained which guarantee that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound. Then the design method of the non-fragile guaranteed cost controller is formulated in terms of the linear matrix inequality (LMI) approach. A numerical example is given to illustrate the effectiveness of the proposed design method.