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Partial stability of a class of large-scale systems with partiallystable isolated subsystems

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Journal of Systems Engineering and Electronics 2005年第2期16卷 346-350页

作者： JianJigui LuoHaigeng LiaoXiaoxin CollegeofScience ChinaThreeGorgesUniversityYichang443002P.R.China//DepartmentofControlSystems&EngineeringHuazhongUniversityofScience&TechnologyWuhan430074P.R.China DepartmentofControlSystems&Engineering HuazhongUniversityofScience&TechnologyWuhan430074P.R.China

The problem of partial stability is investigated for a class of continuous-time large-scale systems. Under assumption that the null solution of the isolated subsystems is stable, based on decomposition-aggregation methods and lyapunov second method, some theorems concerning the globally partial asymptotic stability and globally partial exponential stability are obtained via utilizing the inequality analysis technique and comparison technique. Finally, an example is presented to illustrate the results.

关键词： large-scale systems partial stability inequality comparison principle lyapunov function.

The stability of the positive solution for a fractional SIR model

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International Journal of Biomathematics 2017年第1期10卷 259-272页

作者： Yingjia Guo School of Mathematics and StatisticsBeihua University Jilin 132013 P. R. China

In order to deal with non-differentiable function., a modification of the Riemann- Liouville definition is recently proposed which appears to provide a framework for a fractional calculus which is quite parallel with classical calculus. Based on these new results, we study on the fractional SIR model in this paper. First, we give the general solution of the fractional differential equation. And then a unique global positive solution of the SIR model is obtained. Furthermore, we get the lyapunov stability theory. By using this stability theory, the asymptotic stability of the positive solution is analyzed.

关键词： Fractional SIR epidemic model global stability lyapunov function.

State Feedback Sliding Mode Control without Chattering by Constructing Hurwitz Matrix for AUV Movement

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International Journal of Automation and computing 2011年第2期8卷 262-268页

作者： Huan-Yin Zhou Kai-Zhou Liu Xi-Sheng Feng State Key Laboratory of Robotics Shenyang Institute of Automation Chinese Academy of Sciences Shenyang 110016 PRC School of Electric East China Institute of Technology Fuzhou 344000 PRC Graduate School of the Chinese Academy of Sciences Beijing 100039 RRC

This paper presents a new method to eliminate the chattering of state feedback sliding mode control （SMC） law for the mobile control of an autonomous underwater vehicle （AUV） which is nonlinear and suffers from unknown disturbances system. SMC is a well-known nonlinear system control algorithm for its anti-disturbances capability, while the chattering on switch surface is one stiff question. To dissipate the well-known chattering of SMC, the switching manifold is proposed by presetting a Hurwitz matrix which is deducted from the state feedback matrix. Meanwhile, the best switching surface is achieved by use of eigenvalues of the Hurwitz matrix. The state feedback control parameters are not only applied to control the states of AUV but also connected with coefficients of switching surface. The convergence of the proposed control law is verified by lyapunov function.and the robust character is validated by the Matlab platform of one AUV model.

关键词： Autonomous underwater vehicle (AUV) state feedback sliding mode control (SMC) switching manifold Hurwitz matrix Matlab platform lyapunov function.

The Analysis of Global Input-to-state Stability for Piecewise Affine Systems with Time-delay

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International Journal of Automation and computing 2012年第2期9卷 211-214页

作者： Xiao-Wu Mu Yang Gao Department of Mathematics Zhengzhou University Zhengzhou 450052 PRC Department of Mathematics Daqing Normal University Daqing 163712 PRC

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-lyapunov function. are adopted. Both lyapunov-Razumikhiu and lyapunov-Krasovskii methods are used The theorems of lyapunov-Razumikhin type and lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

关键词： Piecewise affine systems input-to-state stability time delays discrete systems lyapunov function.

DECENTRALIZED STABILIZATION OF A CLASS OF INTERCONNECTED SYSTEMS

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Applied Mathematics(A Journal of Chinese Universities) 2001年第3期16卷 330-338页

作者： Jin Chaoyongof Math.,Shantou Univ.,Guangdong 515063. Dept. of Math. Shantou Univ. Guangdong

This paper is concerned with the decentralized stabilization of continuous and discrete linear interconnected systems with the structural constraints about the interconnection matrices. For the continuous case,the main improvement in the paper as compared with the corresponding results in the literature is to extend the considered class of systems from S to S  (both will be defined in the paper) without resulting in high decentralized gain and difficult numerical computation. The algorithm for obtaining decentralized state feedback control to stable the overall system is presented. The discrete case and some very useful results are discussed as well.

关键词： Interconnected systems decentralized stabilization Riccati equation lyapunov function.

A NOTE ON NONLINEAR ROBUST H_∞ ALMOST DISTURBANCE DECOUPLING PROBLEM WITH STABILITY

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Journal of Systems Science & Complexity 2002年第1期15卷 35-42页

作者： WEIJianfeng ZHENGYufan DepartmentofElectricalEngineeringandComputerScience CaseWesternReserveUniversityClevelandOH44106USA DepartmentofElectricalandElectronicEngineering TheUniversityofMelbourneVic.30

For a class of SISO nonlinear control systems with parameter uncertainty an almost disturbance decoupling problem with stability is defined and investigated. Back stepping technique provides a practical design method of controller, under which the $L2$ gain from the disturbance to the controlled output can be arbitrarily small subject to nonlinear uncertainties and the close-loop system is internally asymptotically stable.

关键词： Nonlinear control systems uncertainty almost disturbance decoupling stability lyapunov function.

ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS

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Journal of Systems Science & Complexity 2002年第1期15卷 85-88页

作者： GANZuoxin ZHAOSuxia 等 InstituteofSystemsScience AcademyofMathematicsandSystemsScienceChineseAcademyofsciencesBeijing100080China InstituteofSystemsScience AcademyofMathematicsandSystemsScienceChineseAcademyofsciencesBe

In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by lyapunov function.approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.

关键词： Absolute stability discrete controlsystems lyapunov function.

STABILITY OF function.L DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

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Applied Mathematics(A Journal of Chinese Universities) 2005年第2期20卷 142-150页

作者： LuoZhiguo ShenJianhua Dept.ofMath. HunanNormalUniv.Changsha410081China

In this paper,the stability of a class of impulsive function.l differential equations with infinite delays is investigated.A uniform stability theorem and a uniform asymptotic stability theorem are established.

关键词： stability Razumikhin technique lyapunov function.

THE ATTRACTORS OF PARTIAL DIFFERENTIAL EQUATIONS

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Applied Mathematics(A Journal of Chinese Universities) 2000年第2期15卷 143-150页

作者： Liu Yingdong\ Li ZhengyuanDept.of Math.,Beijing Univ.,Beijing 1 0 0 871 Dept. of Math. Beijing Univ. Beijing

In this paper the reaction\|diffusion systems and the damped wave systems with nonlinear terms of gradient form are studied,and the conditions for making them to be gradient systems are *** the structure of attractors is clear and simple in some sense by the known *** examples are *** the reaction\|diffusion systems with general nonlinear terms are discussed.

关键词： Global attractor gradient system lyapunov function.