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quadratic stability and H∞ Control of a Class of Uncertainty T-S Fuzzy Systems

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Quadratic Stability and H∞ Control of a Class of Uncertaint...

2011 Chinese Control and Decision Conference（CCDC）

作者： Ying Zhang is with Faculty of Sciences,Shenyang University.Shenyang.110044 Yanan Wang and Ding Zhai are with College of Sciences,Northeastern University.Shenyang.110819.Xiangyong Chen is with School of Information Science and Engineering,Northeastern University.110819,China.

For a class of the uncertainty T-S fuzzy systems,the problem of the quadratic stability and H∞ control is studied in this ***,we give the model of the T-S fuzzy systems,and obtain the conditions for quadratic *** to linear matrix inequalities （LMIs）,we also study the conditions of H∞ control problem,and give the design methods of the state feedback H∞ ***,numerical examples show the feasibility and the effectiveness of the deign method of H∞ control problem.

关键词： T-S fuzzy systems quadratic stability H∞ control linear matrix inequalities (LMIs)

quadratic stability of Uncertain Distributed Parameter Systems

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Quadratic Stability of Uncertain Distributed Parameter Syste...

1994年中国控制会议

作者： Chen Wanyi, Fengsheng Tu Department of Computer and System Sciences, Nankai University Tianjin 300071, P.R.China

＜正＞This note is concerned with the quadratic stability of uncertain distributed parameter systems, in which time-varying unknown-but-bounded parameters come into the state *** the applications of some operator methods, we characterize this stability under a mild assumption, and generalize the related results in the finite dimensional case.

关键词： quadratic stability uncertain systems Co-semigroup

Asymptotically Necessary and Sufficient quadratic stability Conditions of T-S Fuzzy Systems Using Staircase Membership Function and Basic Inequality

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Open Journal of Applied Sciences 2022年第11期12卷 1824-1836页

作者： Jianjian Zeng Lijuan Bao School of Mathematics and Information Science Nanchang Hangkong University Nanchang China

Asymptotically necessary and sufficient quadratic stability conditions of Takagi-Sugeno (T-S) fuzzy systems are obtained by utilizing staircase membership functions and a basic inequality. The information of the membership functions is incorporated in the stability analysis by approximating the original continuous membership functions with staircase membership functions. The stability of the T-S fuzzy systems was investigated based on a quadratic Lyapunov function. The asymptotically necessary and sufficient stability conditions in terms of linear matrix inequalities were derived using a basic inequality. A fuzzy controller was also designed based on the stability results. The derivation process of the stability results is straightforward and easy to understand. Case studies confirmed the validity of the obtained stability results.

关键词： Takagi-Sugeno Fuzzy System quadratic stability Fuzzy Controller Staircase Membership Function

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

stability and Stabilization of Block-cascading Switched Linear Systems

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International Journal of Automation and computing 2006年第4期3卷 404-413页

作者： Ya-Hong Zhu Dai-Zhang Cheng Institute of Systems Science Chinese Academy of Sciences Beijing PRC

The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the common cascading form, a common quadratic Lyapunov function is （QLFs） is explored by finding common QLFs of diagonal blocks. In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.

关键词： Switching linear system quadratic stability common quadratic Lyapunov function reducible Lie algebra,cascading Quaker Lemma

DELAY DEPENDENT ROBUST DISSIPATIVE CONTROL FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS

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Annals of Differential Equations 2005年第3期21卷 497-502页

作者： Yang Li Zhang Qingling Liu Guoyi Liu Peiyong Institute of System Science Noriheastern University Shenyang 110004 Biotechnology Institute Northeastern University Shenyang 110004

We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities （LMIs）, then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.

关键词： nonlinear perturbation time-delay systems delay dependent robust dissipative quadratic stability

Optimal Guaranteed Cost Control via Static Output Feedback for Uncertain Discrete Time Systems

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Journal of Beijing Institute of Technology 1999年第2期8卷 77-84页

作者：吴淮宁费元春北京理工大学电子工程系

Aim To study the optimal guaranteed cost control problem via static output feedback for uncertain linear discrete time systems with norm bounded parameter uncertainty in both the state and the control input matrices of the state space model. Methods\ An upper bound on a quadratic cost index was found for all admissible parameter uncertainties and minimized by using Lagrange multiplier approach. Results and Conclusion\ Sufficient conditions are given for the existence of a controller guaranteeing the closed loop system quadratic stability and providing an optimized bound. A numerical algorithm for solving the output feedback gain is also presented.

关键词： linear discrete systems robust control static output feedback quadratic stability

Feedback Control for quadratic Nonlinear Systems

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Feedback Control for Quadratic Nonlinear Systems

第24届中国控制与决策会议

作者： Luis Alvergue Department of Electrical and Computer Engineering Louisiana State UniversityBaton Rouge Louisiana USA.

We propose two state feedback control strategies based on quadratic stability for quadratic nonlinear systems, specifically reduced order fluid flow models. Stabilizing linear controllers are designed at each operating point, but unlike traditional linear designs, the nonlinear dynamics are taken into account during the design process by representing them as elements of a bounding set. By solving a set of linear matrix inequalities an estimate of the region of attraction at each operating point of the closed loop system is presented. The overall design consists of a sequence of linear controllers that regionally stabilize and enlarge the region of attraction of the desired operating points. Under the assumption that the system admits a centered- -cover, a switching strategy is proposed that achieves semiglobal stabilization of the nonlinear system.

关键词： nonlinear systems quadratic stability flow control LMI

Passive Control for Uncertain Singular Bilinear Systems

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Passive Control for Uncertain Singular Bilinear Systems

2009中国控制与决策会议

作者： Dongmei Yang~1,Qiongyan Xiong ~1,Yan Wang~1,Ding Zhai~1 1.School of Science,Northeastern University,Shenyang,110004

The passive control problem is discussed under bounded energy exogenous inputs by means of linear matrix inequalities and generalized algebra Riccati inequalities,and a sufficient condition is derived as such that a prescribed uncertain singular bilinear system is admissible and strictly ***,the design method for state feedback controller is also given.

关键词： singular bilinear system quadratic stability strictly passive control state feedback passive control