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Membership-Function-Dependent Stability Conditions Using Fuzzy Lyapunov Functions
Kyung Soo Kim,Ho Sub Lee,PooGyeon Park 제어로봇시스템학회 2022 제어로봇시스템학회 국제학술대회 논문집 Vol.2022 No.11
This paper proposes the membership-function-dependent stability conditions for T-S fuzzy systems using fuzzy Lyapunov functions. The properties of both membership functions (MFs) and the derivative of MFs are utilized to obtain the stability condition of the fuzzy system. The fuzzy Lyapunov functions are employed for stability analysis to exploit the information of the derivative of MFs. For achieving the less conservative stability result, the convex polytopes capturing the distributions of MFs and the derivative of MFs provide the stability condition in the shape of linear matrix inequalities. Under the same fuzzy Lyapunov function, two different way to derive the stabilization condition is investigated. Simulation shows the effectiveness of the proposed approach compared with the previous method, which is a quadratic Lyapunov function.
시간 종속적인 리아프노프 함수를 이용한 모바일 로봇의 선도-추종 샘플 데이터 제어
예동희,한승용,이상문,Ye, Donghee,Han, Seungyong,Lee, Sangmoon 대한임베디드공학회 2021 대한임베디드공학회논문지 Vol.16 No.4
The aim of this paper is to propose a less conservative stabilization condition for leader-following sampled-data control of wheeled mobile robot (WMR) systems by using a clock-dependent Lyapunov function (CDLF) with looped functionals. In the leader-following WMR system, the state and input of the leader robot are measured by digital devices mounted on the following robot, and they are utilized to construct the sampled-data controller of the following robot. To design the sampled-data controller, a stabilization condition is derived by using the CDLF with looped functionals, and formulated in terms of sum of squares (SOS). The considered Lyapunov function is a polynomial form with respect to the clock related to the transmitted sampling instants. As the degree of the Lyapunov function increases, the stabilization condition becomes less conservative. This ensures that the designed controller is able to stabilize the system with a larger maximum sampling interval. The simulation results are provided to demonstrate the effectiveness of the proposed method.
Yukun Tao,Feifei Yang,Ping He,Congshan Li,Yuqi Ji 제어·로봇·시스템학회 2020 International Journal of Control, Automation, and Vol.18 No.9
This paper presents a distributed adaptive neural tracking consensus control strategy for a class of stochastic nonlinear multiagent systems with whole state time delays, input and output constrains. The considered systems are involved in the existence of whole state delays and stochastic disturbances, which makes the controller design more difficult and complex. Firstly, time delays are related to unknown dynamic interactions with the whole states of the agent systems, and novel Lyapunov-Krasovskii functionals are constructed. Secondly, the smooth asymmetric saturation nonlinearity is given based on Gaussian error function, output constraints are achieved via barrier Lyapunov functions, and neural networks are utilized to deal with the completely unknown nonlinearities and stochastic disturbances. Then, based on Lyapunov stability theory, a delay-independent adaptive controller is developed via Lyapunov-Krasovskii functionals and backstepping technique, and it reduces the complexity of learning parameters. It is proved that the proposed approximation-based controller can guarantee that all closed-loop signals are cooperatively semi-globally uniformly ultimately bounded (CSGUUB), and the tracking errors between the followers and the leaders eventually converge to a small neighbourhood around the origin. Finally, simulation studies are carried out, and the simulation results verify the correctness and effectiveness of the proposed Strategy.
퍼지 리아푸노프 함수를 이용한 어파인 퍼지 시스템의 완화된 안정도 조건
김대영(Dae Young Kim),박진배(Jin Bae Park),주영훈(Young Hoon Joo) 대한전기학회 2012 전기학회논문지 Vol.61 No.10
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.
불완전한 전반부 정합 하에서의 이산 T-S 퍼지 모델에 대한 완화된 안정화 조건
임현준(Hyeon Jun Lim),주영훈(Young Hoon Joo),박진배(Jin Bae Park) 한국지능시스템학회 2017 한국지능시스템학회논문지 Vol.27 No.1
본 논문은 이산 Takagi-Sugeno (T-S) 퍼지 모델의 제어기 설계 시 시스템과 제어기가 상이한 소속 함수를 가지는 불완전한 전반부 정합 하에서의 제어기 설계에 대해 다룬다. 이산 T-S 퍼지 모델의 안정화 조건을 구할 때, 단일 Lyapunov 함수를 이용하여 구한 기존의 보수적인 안정화 조건보다 완화된 안정화 조건을 구하기 위해 퍼지 Lyapunov 함수를 고려한다. 퍼지 Lyapunov 함수를 이용하여 선형 행렬 부등식 기반의 완화된 안정화 조건을 구하고 시뮬레이션을 통해 제안한 방법의 타당성을 검증한다. In this paper, a controller for discrete Takagi-Sugeno(T-S) fuzzy model under imperfect premise matching is proposed. Most of previous papers have obtained the stabilization condition using common quadratic Lyapunov function. However, the stabilization condition may be conservative due to the typical disadvantage of the common quadratic Lyapunov function. Hence, in order to solve this problem, we propose the stabilization condition of discrete T-S fuzzy model using fuzzy Lyapunov function. Finally, the proposed approach is verified by the simulation experiments.
Lyapunov functions for nonlinear difference equations
최성규,최은화,구남집 충청수학회 2011 충청수학회지 Vol.24 No.4
In this paper we study h-stability of the solutions of nonlinear difference system via the notion of n_∞-summable similarity between its variational systems. Also, we show that two concepts of h-stability and h-stability in variation for nonlinear difference systems are equivalent. Furthermore, we characterize h-stability for nonlinear difference systems by using Lyapunov functions.
불확실성과 시변 입력 지연이 있는 Ball and Beam 시스템의 제어기 설계
김승호,김영재,이용권,이승훈,김성동,권오민 제어로봇시스템학회 2021 제어로봇시스템학회 국내학술대회 논문집 Vol.2021 No.6
This paper deals with a controller design for a linear system with a time-varying delay and uncertainties. The stability condition is derived in the forms of linear matrix inequalities through the construction of Lyapunov-Krasovskii functionals and the use of mathematical techniques. Applying the main result and Beam system example, the effectiveness of uncertainties and time-varying input delay for the system is confirmed.
Lyapunov Conditions for Finite-time Stability of Stochastic Functional Systems
Jian Ge,Liping Xie,Shixiong Fang,Kanjian Zhang 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.1
In this study, we consider the finite time stability (FTS) and finite time contractive stability (FTCS) of the stochastic functional systems. For the framework of Lyapunov-Ruzumikhin method, the sufficient conditions of FTS and FTCS are given first. Then the theory is applied to FTS and FTCS of linear time-varying stochastic functional systems. Finally, experiments on the numerical examples have demonstrated the superiority of the proposed method.
Improved Robust Passivity Criteria for Delayed Neural Networks
Yaqi Li,Shuangcheng Sun,Yun Chen 제어·로봇·시스템학회 2024 International Journal of Control, Automation, and Vol.22 No.3
This paper investigates the robust passivity problem for neural networks with uncertain system parameters and a time-varying delay. Based on Lyapunov stability theory, ensuring the negative definiteness for the derivatives of the developed Lyapunov-Krasovskii functional (LKF) is necessary in order to derive a passivity criterion. Anegative condition on the cubic polynomial over a certain interval is developed in this paper, which introduces someslack matrices to obtain an advanced negative condition. Taking advantage of this condition, an augmented LKFwith more system state and delay function information, including several augmented vectors and a single-integralbased term, is constructed. Then some improved passivity criteria for delayed neural networks are derived on topof the proposed LKF and the negative condition. Finally, the effectiveness and superiority of the obtained passivitycriteria are validated on two numerical examples.
엄기환,박장환,이용구 동국대학교 산업기술연구원 1995 산업기술논문집 Vol.6 No.-
Lur'e 판별법으로부터 비선형소자 포화를 갖는 이산제어시스템의 안정도를 위한 Lyapunov 함수를 구성하고 이를 안정도 판별에 활용했다. 연속시스템에서의 Lur'e 판별법을 근거로 Popov 판별식이 유도되어지는 것과 같이, 이산 제어 시스템에서는 비선형소자 포화를 이산화함으로써 Zypkin 판별법이 유도되어 질 수 있었다. 시간영역과 주파수영역 사이의 안정도관계는 Lyapunov 함수의 존재를 근거로 하여, Kalman-Szego¨ 보조정리와 Zypkin 판별법을 유도하였다. In this paper, it is shown that the construction and application of Lyapunov-function for stability of non-linear discrete control system within on-linearity "saturation" from Lur'e-Criterion. The derivation of Popov-criterion is based on the Lur'e-criterion. In discrete control system, the derivation of Tzypkin-criterion is possible to discrization non-linearity element "saturation". Kalman-Szego¨-lemma and Tzypkin-criterion which the stability relationship between frequency domain and time domain representation, is derived based on the existence of Lyapunov-function.