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finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects

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Journal of Systems Engineering and Electronics 2010年第2期21卷 254-260页

作者： Ying Yang Junmin Li Guopei Chen Department of Applied Mathematics Xidian University Xi'an 710071 R R. China Department of Mathematics Huizhou University Huizhou 516007 R R. China

Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finite-time stab!lity analysis are investigated for a class of Markovian switching stochastic sys- tems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop sys- tems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffu- sion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities （LMIs）. A numerical example is presented to illustrate the proposed methodology.

关键词： finite-time stability impulsive systems Markovian switching Brownian motion linear matrix inequalities (LMIs) sta- bilization.

finite-time stability of Fractional-Order Neural Networks with Delay

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Communications in Theoretical Physics 2013年第8期60卷 189-193页

作者：吴然超黑鑫东陈立平 School of Mathematics Anhui University School of Automation Chongqing University

finite-time stability of a class of fractional-order neural networks is investigated in this paper. By Laplace transform, the generalized Gronwa11 inequality and estimates of Mittag-Leffier functions, sufficient conditions are pre- sented to ensure the finite-time stability of such neural models with the Caputo fractionM derivatives. Furthermore, results about asymptotical stability of fractional-order neural models are also obtained.

关键词： neural networks fractional-order finite-time stability Gronwall inequality

finite-time stability and Instability of Nonlinear Impulsive Systems

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Advances in Applied Mathematics and Mechanics 2023年第1期15卷 49-68页

作者： Guihua Zhao Hui Liang College of Science University of Shanghai for Science and TechnologyShanghai200093China School of Science Harbin Institute of TechnologyShenzhenGuangdong 518055China

In this paper,the finite-time stability and instability are studied for nonlinear impulsive *** are mainly four concerns.1)For the system with stabilizing impulses,a Lyapunov theorem on global finite-time stability is presented.2)When the system without impulsive effects is globally finite-time stable(GFTS)and the settling time is continuous at the origin,it is proved that it is still GFTS over any class of impulse sequences,if the mixed impulsive jumps satisfy some mild conditions.3)For systems with destabilizing impulses,it is shown that to be finite-time stable,the destabilizing impulses should not occur too frequently,otherwise,the origin of the impulsive system is finite-time instable,which are formulated by average dwell time(ADT)conditions respectively.4)A theorem on finite-time instability is provided for system with stabilizing *** each GFTS theorem of impulsive systems considered in this paper,the upper boundedness of settling time is given,which depends on the initial value and impulsive *** numerical examples are given to illustrate the theoretical analysis.

关键词： Impulsive systems finite-time stability finite-time instability nonlinear systems

finite-time stability and Stabilization of Discrete-time Switching Markov Jump Linear System

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Journal of Shanghai Jiaotong university(Science) 2020年第5期25卷 674-680页

作者： JIN Yunyun SONG Yang LIU Yongzhuang HOU Weiyan Department of Automation School of Mechatronics Engineering and AutomationShanghai UniversityShanghai 200444China Shanghai Key Laboratory of Power Station Automation Technology Shanghai UniversityShanghai 200444China School of Information Engineering Zhengzhou UniversityZhengzhou 450001China

Switching Markov jump linear system(SMJLS),a special hybrid system,has attracted a lot of studies *** is governed by stochastic and deterministic *** paper focuses on the switching strategy which stabilizes the SMJLS in a finite time interval in order to further expand the existing results and investigate new aspects of such *** sufficient conditions for finite-time stability of discrete-time SMJLS are provided,and the numerical problems in these sufficient conditions are solved by solving linear matrix inequalities(LMIs).Finally,numerical examples are given to show the feasibility and effectiveness of the results.

关键词： switching Markov jump linear system(SMJLS) finite-time stability stochastic switching deterministic switching minimum dwell time

finite-time stability of switched linear systems

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Finite-time stability of switched linear systems

finite-time stability for Nonlinear Fractional Differential Equations with time Delay

第36届中国控制会议

作者： Linlin Hou Chuanguang Sun Hangli Ren Yunliang Wei School of Control Science and Engineering Dalian University of Technology School of Information Science and Engineering Qufu Normal University Basic Teaching Department ShanDong Water Conservancy Vocational College School of Engineering Qufu Normal University School of Mathematical Sciences Qufu Normal University

ISBN: (纸本)9781538629185

In this paper, the problem of finite-time stability is studied for a class of switched linear systems, where some subsystems are not finite-time stable. A novel average dwell time approach for finite-time stability of switched linear systems in which not all subsystems are finite-time stable is first proposed. Moreover, by constructing a new multiple Lyapunov functional, sufficient condition is provided to cope with the problem of finite-time stability for the given systems. Finally, a numerical example is illustrated to show the effectiveness of the proposed results.

关键词： Switched linear systems average dwell time finite-time stability

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Journal of Donghua University(English Edition) 2022年第5期39卷 446-453页

作者： HE Huazhen KOU Chunhai College of Science Donghua UniversityShanghai 201620China

The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions of the considered system is defined in terms of the Caputo fractional Dini derivative. Based on the Lyapunov-Razumikhin method, several sufficient criteria are established to guarantee the finite-time stability and the finite-time contractive stability of solutions for the related systems. An example is provided to illustrate the effectiveness of the obtained results.

关键词： finite-time stability nonlinear fractional differential equation time delay Caputo fractional Dini derivative Lyapunov-Razumikhin method

finite-time stability for Markovian Jump Nonlinear Systems with Random Delays

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Finite-Time Stability for Markovian Jump Nonlinear Systems w...

finite-time stability of stochastic nonlinear systems with Markovian switching

第36届中国控制会议

作者： CHEN Haiyang LIU Meiqin ZHANG Senlin State Key Laboratory of Industrial Control Technology Zhejiang University College of Electrical Engineering Zhejiang University

ISBN: (纸本)9781538629185

This paper investigates the stochastic finite-time stability（SFTS） problem for a class of Markovian jump nonlinear systems with time delays. The nonlinear terms are assumed to satisfy the Lipschitz conditions, and the time delays are modelled by mutually independent stochastic variables subject to Bernoulli distributions. The aim of our work is to design a set of linear feedback controllers such that the addressed system is SFTS in the presence of Markov jumps, random delays, and *** our work, first the SFTS performances are analyzed by virtue of Lyapunov functional and stochastic control strategy. Then according to these analyses, new criterion are given in terms of linear matrix inequalities（LMIs） in order to design the feedback controller. In addition, a reasonable strategy is proposed to reduce the resource consumption of controller design. And the effect of random delays on control performances is also discussed. Finally, an illustrative example is provided to validate the proposed method.

关键词： Markovian jump nonlinear systems stochastic control random delays finite-time stability Bernoulli distribution

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Finite-time stability of stochastic nonlinear systems with M...

Controlling chaos in power system based on finite-time stability theory

第36届中国控制会议

作者： Juliang Yin Xin Yu Suiyang Khoo Department of Statistics Jinan University School of Electrical and Information Engineering Jiangsu University School of Engineering Deakin University

ISBN: (纸本)9781538629185

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation（SDE） systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari’s inequality are derived,which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.

关键词： finite-time stability Lyapunov stability Stochastic nonlinear systems Markovian switching

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Chinese Physics B 2011年第12期20卷 101-108页

作者：赵辉马亚军刘思佳高士根钟丹 Tianjin Key Laboratory for Control Theory and Applications in Complicated Systems Tianjin University of Technology School of Electronic and Information Engineering Beijing Jiaotong University School of Electrical Engineering and Automation Tianjin University

Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse, which severely threatens the secure and stable operation of the power system. Based on the finite-time stability theory, two control strategies are presented to achieve finite-time chaos control. In addition, the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time. Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme. The research in this paper may help to maintain the secure operation of power systems.

关键词： power system chaos control finite-time stability stabilize unstable nonzero equilibrium point robust controller