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Wenpin Luo,Jun Yang,Xin Zhao 제어·로봇·시스템학회 2016 International Journal of Control, Automation, and Vol.14 No.4
This paper focuses on further improved stability criteria for uncertain T-S fuzzy systems with timevaryingdelay by delay-partitioning approach and Free-Matrix-based integral inequality. A modified augmentedLyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then, on thebasis of taking into account the independent upper bounds of the delay derivative in various delay intervals, somenew results on tighter bounding inequalities, such as Peng-Park’s integral inequality and the Free-Matrix-basedintegral inequality are employed to effectively reduce the enlargement in bounding the derivative of LKF, therefore,less conservative results can be expected in terms of es and LMIs. Finally, three numerical examples are includedto show that the proposed method is less conservative than existing ones.
Robust Stabilization of Singular Markovian Jump Systems with Uncertain Switching
Guo-Liang Wang 제어·로봇·시스템학회 2013 International Journal of Control, Automation, and Vol.11 No.1
This paper focuses on the robust stabilization problem for a class of singular Markovian jump systems with uncertain switching probabilities. Based on a slack matrix method on transition probabilities, a new criterion for quadratically stochastic admissibility of such an uncertain system is established. Then, two new sufficient conditions for the existence of mode-dependent controller are given as linear matrix inequalities. Especially, a more practical controller named as mode-independent controller is derived by a mode-dependent Lyapunov function. Finally, a numerical example is used to demonstrate the effectiveness of the proposed methods.
Haiyang Zhang,Lianglin Xiong,Qing Miao,Yanmeng Wang 제어로봇시스템학회 2015 제어로봇시스템학회 국제학술대회 논문집 Vol.2015 No.10
This article addressed the problem of delay-dependent stability criteria for linear time system with interval time-delay. Firstly, we proposed a new inequality based on the Fourier Theory, more precisely on theWirtingers inequalities, which is proved to encompass the Jensens inequality. Secondly, a less conservative stability condition is established in terms of linear matrix inequalities by employing delay-partition idea and Lyapunov functional method. Finally, in order to illustrate the potential gain of employing this new inequality with respect to the Jensens one and the effectiveness of the proposed results,an application to time-delay analysis is provided.
Reachable Set Estimation for Itô Stochastic Semi-Markovian Jump Systems Against Multiple Time Delays
Shaoxin Sun,Xin Dai,Ruipeng Xi,Yuliang Cai,Xiangpeng Xie,Chunhua Zhang 제어·로봇·시스템학회 2022 International Journal of Control, Automation, and Vol.20 No.9
The work deals with these issues of stochastic finite-time boundedness (SFTB), reachable set estimation with input-output finite-time mean square stabilization (IO-FTMSS) for multiple state delayed semi-Markovian jump models subject to uncertainties, stochastic process as well as input constraint. There are few attempts to perform related studies. Firstly, a nonlinear passive control mechanism is designed. Then, a closed-loop model could be acquired. Through stochastic Lyapunov function, these problems of SFTB, reachable set estimation with IO-FTMSS could be solved. In addition, these stability conditions are provided in the framework of linear matrix inequalities. These controller gain matrices, meanwhile, can be derived. At last, this availability of this described strategy can be proved through one simulation.
Song, M.K.,Park, J.B.,Joo, Y.H. North-Holland 2015 Fuzzy Sets and Systems Vol. No.
This paper presents a new methodology of robust state feedback fuzzy controller based on free weighting matrix method for a class of uncertain Markovian jump nonlinear systems. The class of systems under consideration is represented by the T-S fuzzy model with partly known transition probability matrix. The free weighting matrix method is proposed to obtain a less conservative stochastic stability criterion of the uncertain Markovian jump fuzzy systems (MJFSs) in terms of linear matrix inequalities (LMIs). Furthermore, a sufficient condition for the mode-dependent state feedback fuzzy controller is derived for the MJFSs for all admissible parameter uncertainties. Finally, a simulation example is provided to illustrate the effectiveness of the proposed methodology.
BIBO Stabilization of T-S Fuzzy Neutral Systems by LMI Approach
Guihua Li,Jun Yang,Yan Zeng 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.4
In this paper, the problem of bounded-input bounded-output (BIBO) stabilization for a class of Takagi-Sugeno (T-S) fuzzy neutral systems is considered. Based on the Lyapunov-Krasovskii func-tional, the descriptor model transformation and the linear matrix inequality (LMI) approach, sufficient conditions guaranteeing BIBO stabilization of the T-S fuzzy neutral systems are established in terms of LMIs. And an explicit expression of the desired controller is readily given when these LMIs are feasible. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed approach.
Jing Chen,Ji-Qing Qiu,Peng Shi,Hong-Jiu Yang 제어·로봇·시스템학회 2010 International Journal of Control, Automation, and Vol.8 No.2
In this paper, the problem of stochastic robust stability of time-varying delay neutral system with Markovian jump parameters is investigated. The jumping parameters are considered as a continuous-time, continuous state Markov process. Based on the Lyapunov-Krasovskii functional approach, a new delay-dependent stochastic stability criteria is presented in terms of LMIs. A numerical example is given to illustrate the effectiveness of the developed method.
Chao Ge,Chang-chun Hua,Xin-Ping Guan 제어·로봇·시스템학회 2014 International Journal of Control, Automation, and Vol.12 No.4
This paper concerns with the problem of asymptotic stability for neutral systems with time-varying delays. With the introduction of delay-decomposition approach, some new delay-dependent stability criteria are established and formulated in the form of linear matrix inequalities. Both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.
Generalized Multiple Delay-dependent H∞ Functional Observer Design for Nonlinear System
Ghali Naami,Mohamed Ouahi,Teresa Alvarez,Abdelhamid Rabhi 제어·로봇·시스템학회 2023 International Journal of Control, Automation, and Vol.21 No.11
Functional observers are the major alternative to many practical estimation problems where full-order observers cannot be used. This paper introduces a generalized approach to design H∞ functional observers for a class of Lipschitz nonlinear systems with multiple time delays. Moreover, the considered system extends from previously published work in that it presents nonlinearity, multiple delay and external disturbance. Their main findings come from the development of a generalized augmented Lyapunov function that uses both the extended reciprocal convex combination and the Wirtinger inequality. The stability of the observer is therefore guaranteed by an LMI optimization problem. Finally, the steps of the design procedure were condensed and proffered for the two numerical examples to test the recommended design approach.
Robust H_∞ DOF Control for Uncertain T-S Fuzzy Neutral Systems
Wenpin Luo,Jun Yang,Li Xiang,Shouming Zhong 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.3
This paper investigates the problem of robust H_∞ dynamic output-feedback (DOF) control for a class of uncertain T-S fuzzy neutral systems with linear fractional parametric uncertainties. The aim is to design a full-order fuzzy DOF controller that ensures asymptotic stability of the closed-loop system and guarantees a prescribed H_∞ performance level on disturbance attenuation for all admissible uncertainties. Based on the Lyapunov-Krasoviskii functional and the Barbalat lemma, delay-dependent sufficient conditions for the solvability of this problem are presented in terms of LMIs. Finally, a simulation example is provided to demonstrate the effectiveness and applicability of the proposed method.