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parameter-dependent lyapunov function Method Applied to Satellite Formation Keeping Control

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Parameter-Dependent Lyapunov Function Method Applied to Sate...

第二十七届中国控制会议

作者： Yue Xincheng,Yang Ying,Duan Zhisheng,Geng Zhiyong State Key Laboratory for Turbulence and Complex System,Department of Mechanics and Aerospace Technology,College of Engineering,Peking University,Beijing 100871,P.R.China

In this paper,a parameter-dependent lyapunov function method is applied to design robust controller for a satellite formation flying system around the Earth based on an uncertainty model derived from a nonlinear relative position *** this model,nonzero eccentricity and varying semi-major axis are included as parametric *** perturbations including J2 perturbation,atmospheric drag and actuation are bounded by functional *** model can be regarded as a polytopic type uncertain system with 8 vertices,then the parameter-dependent lyapunov function is proposed to design H2 and H∞controllers respectively to maintain the relative position of the formation flying *** simulation demonstrates that the proposed controller can realize the control the satellites formation-keeping.

关键词： parameter-dependent lyapunov function Satellite Formation Keeping Polytope Linear Matrix Inequality (LMI)

Fuzzy Constrained MPC Output Feedback Controller Design for Nonlinear Systems Based on parameter-dependent lyapunov function Approach

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Fuzzy Constrained MPC Output Feedback Controller Design for ...

第25届中国控制与决策会议

作者： Hui-Wei Liu Ke-Zhen Han Xiao-Heng Chang College of Engineering Bohai University

ISBN: (纸本)9781467355339

The fuzzy constrained MPC output feedback control problem for a class of discrete-time T-S fuzzy systems is studied in this paper. Generally, based on the parameter dependent lyapunov function approach, the controller design conditions are given in the form of LMIs via using parallel distribution compensation （PDC） techniques. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

关键词： Discrete-time T-S fuzzy systems parameter-dependent lyapunov function PDC technology MPC static output feedback control

Robust H-infinity filtering for uncertain discrete-time systems using parameter-dependent lyapunov functions

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控制理论与应用（英文版） 2013年第1期11卷 122-127页

作者： Xiaoheng CHANG Guanghong YANG College of Engineering Bohai University Key Laboratory of Integrated Automation for the Process Industry Ministry of Education and College of Information Science and Engineering Northeastern University

This paper deals with H-infinity filtering of discrete-time systems with polytopic uncertainties. The un- certain parameters are supposed to reside in a polytope. By using the parameter-dependent lyapunov function approach and introducing some slack matrix variables, a new sufficient condition for the H-infinity filter design is presented in terms of solutions to a set of linear matrix inequalities （LMIs）. In contrast to the existing results for H-infinity filter design, the main advantage of the proposed design method is the reduced conservativeness. An example is provided to demonstrate the effectiveness of the proposed method.

关键词： Discrete-time systems H-infinity filtering parameter-dependent lyapunov function Linear matrix in- equalities (LMIs)

Robust L_1 filtering with pole constraint in a disk via parameter-dependent lyapunov functions

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Journal of Systems Engineering and Electronics 2005年第1期16卷 102-109页

作者： LiYanhui WenQiyong WangJunling WangChanghong GaoHuijun DepartmentofControlScienceandEngineering HarbinInstituteofTechnologyHarbin150001P.R.China//ElectricalandInformationEngineeringCollegeDaqingPetroleumInstituteDaqing163318P.R.China DepartmentofControlScienceandEngineering HarbinInstituteofTechnologyHarbin150001P.R.China

The problem of robust L 1 filtering with pole constraint in a disk for linear continuous polytopic uncertain systems is discussed. The attention is focused on design a linear asymptotically stable filter such that the filtering error system remains robustly stable, and has a L 1 performance constraint and pole constraint in a disk. The new robust L 1 performance criteria and regional pole placement condition are obtained via parameter-dependent lyapunov functions method. Upon the proposed multiobjective performance criteria and by means of LMI technique, both full-order and reduced-order robust L 1 filter with suitable dynamic behavior can be obtained from the solution of convex optimization problems. Compared with earlier result in the quadratic framework, this approach turns out to be less conservative. The efficiency of the proposed technique is demonstrated by a numerical example.

关键词： robust filtering parameter-dependent lyapunov function linear matrix inequality L 1 performance pole placement technique.

Robust exponential stability and stabilization of linear uncertain polytopic time-delay systems

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控制理论与应用（英文版） 2008年第2期6卷 163-170页

作者： Nam PHAN T. Phat VU N. Department of Mathematics Quynhon UniversityQuynhonBinhdinhVietnam Institute of Mathematics 18 Hoang Quoc Viet RoadHanoiVietnam

This paper proposes new sufficient conditions for the exponential stability and *** linear uncertain polytopic time-delay systems. The conditions for exponential stability are expressed in terms of Kharitonov-type linear matrix inequalities （LMIs） and we develop control design methods based on LMIs for solving stabilization problem. Our method consists of a combination of the LMI approach and the use of parameter-dependent lyapunov functionals, which allows to compute simultaneously the two bounds that characterize the exponetial stability rate of the solution. Numerical examples illustrating the conditions are given.

关键词： Polytopic time-delay system Exponential stability Stabilization parameter-dependent lyapunov function Linear matrix inequalities

An improved robust stability and robust stabilization method for linear discrete-time uncertain systems

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控制理论与应用（英文版） 2007年第1期5卷 99-103页

作者： Xianming ZHANG Min WU Jinhua SHE Dongsheng HAN School of Information Science and Engineering Central South University Changsha Hunan 410083 China School of Mathematical Science and Computing Technology Central South University Changsha Hunan 410083 China School of Bionics Tokyo University of Technology Tokyo 192-0982 Japan Faculty of Business and Informatics Central Queensland University Rockhampton 4702 Australia

This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties. A new and simple method is presented to directly decouple the lyapunov matrix and the system dynamic matrix. Combining this method with the parameter-dependent lyapunov function approach yields new criteria that include some existing ones as special cases. A numerical example illustrates the improvement over the existing ones.

关键词： Robust stability Robust stabilization parameter-dependent lyapunov function Linear matrix inequality

LMI conditions for quadratic and robust D-stability of interval systems

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控制理论与应用（英文版） 2006年第2期4卷 187-192页

作者： Weijie MAO Xu WANG National Lab of Industrial Control Technology Institute of Advanced Process Control Zhejiang University Hangzhou Zhejiang 310027 China

Sufficient conditions for the quadratic D-stability and further robust D-stability of interval systems are presented in this paper. This robust D-stability condition is based on a parameter-dependent lyapunov function obtained from the feasibility of a set of linear matrix inequalities （LMIs） defined at a series of partial-vertex-based interval matrices other than the total vertex matrices as in previous results. The results contain the usual quadratic and robust stability of continuous-time and discrete-time interval systems as particular cases. The illustrative example shows that this method is effective and less conservative for checking the quadratic and robust D-stability of interval systems.

关键词： interval systems Linear matrix inequality (LMI) parameter-dependent lyapunov function Quadratic stability Robust stability

An LMI Approach to HH∞ Filtering of Uncertain Systems

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An LMI Approach to HH∞ Filtering of Uncertain Systems

第24届中国控制与决策会议

作者： Liang Hong 1 , Xiao-Heng Chang 2 1. School of mechanical Electronic and Information Engineer, China University of Mining and Technology, Beijing, 100083, China.2. College of Engineering, Bohai University, Jinzhou, 121003, China.

This paper studies the H∞ filtering problem of linear uncertain systems with polytopic uncertainties. By introducing some slack matrices and using the parameter-dependent lyapunov function approaches, sufficient conditions for the existence of such filter are expressed in terms of linear matrix inequalities （LMIs）. And, a convex analysis procedure is implemented to derive the filter gain matrices. Finally, a numerical example is presented to illustrate the theoretical developments.

关键词： Uncertain systems parameter-dependent lyapunov function slack matrices H∞ filtering Linear matrix inequalities (LMIs)

An Improved Approach to Robust H2 and H∞ Filter Design for Uncertain Linear Systems with Time-varying parameters

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An Improved Approach to Robust H2 and H∞ Filter Design for ...

第二十六届中国控制会议

作者： Xu Jun1,Xie Lihua 2 1.Temasek Laboratories,National University of Singapore,5 Sports Drive 2,Singapore 1175082.School of Electrical and Electronic Engineering,Nanyang Technological University,Nanyang Avenue,Singapore 639798

In this paper,we discuss the robust H2 and H∞ filter problems for a class of continuous-time and discrete-time linear systems with convex bounded uncertain time-varying *** employing parameter-dependent lyapunov functions,some improved sufficient conditions based on a scaling LMI formulation for the robust filtering problems are presented.A numerical example is given to demonstrate the effectiveness of the proposed design methods.

关键词： Robust filter linear matrix inequality (LMI) parameter-dependent lyapunov function