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Delay-dependent stability of two-dimensional Markovian jump systems in the roesser model with interval time-varying delays 36

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Delay-dependent stability of two-dimensional Markovian jump ...

第36届中国控制会议

作者： Jing Zhang Dan Peng Changchun Hua College of Science Yanshan University Institute of Electrical Engineering Yanshan University

ISBN: (纸本)9781538629185

This paper is concerned with the problem of stochastic stability analysis of discrete-time two-dimensional Markovian jump systems（2D MJSs） described by the roesser model. The systems under consideration are subject to interval time-varying and full known transition probabilities of the jumping process/Markov chain. First, new finite-sum inequalities are proposed in this paper. Then giving the Lyapunov-Krasovskii functional（LKF） with time-delay and differencing it via new finite-sum inequalities, delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities（LMIs）. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.

关键词： Two-dimensional Markovian jump systems(2D MJSs) roesser model New finite-sum inequalities Interval timevarying delays Stochastic stability

Stability analysis of nonlinear roesser-type two-dimensional systems via a homogenous polynomial technique

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Chinese Physics B 2012年第12期21卷 109-117页

作者：张铁岩赵琰解相朋 Department of Electrical Engineering Shenyang Institute of Engineering

This paper is concerned with the problem of stability analysis of nonlinear roesser-type two-dimensional （2D） systems. Firstly, the fuzzy modeling method for the usual one-dimensional （1D） systems is extended to the 2D ease so that the underlying nonlinear 2D system can be represented by the 2D Takagi Sugeno （TS） fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conser- vative stability conditions for the TS roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.

关键词： stability analysis roesser model two-dimensional nonlinear systems parameter- dependent Lyapunov function

Stability analysis and control synthesis of uncertain roesser-type discrete-time two-dimensional systems

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Chinese Physics B 2013年第3期22卷 79-84页

作者：王佳会国涛解相朋 School of Mechanical and Vehicular Engineering Beijing Institute of Technology School of Information Science and Engineering Northeastern University

We study the stability analysis and control synthesis of uncertain discrete-time two-dimensional（2D） *** mathematical model of the discrete-time 2D system is established upon the well-known roesser model,and the uncertainty phenomenon,which appears typically in practical environments,is modeled by a convex bounded（polytope type） uncertain *** stability analysis and control synthesis of uncertain discrete-time 2D systems are then developed by applying the Lyapunov stability *** the processes of stability analysis and control synthesis,the obtained stability/stabilzaition conditions become less conservative by applying some novel relaxed ***,the obtained results are formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical ***,numerical examples are given to demonstrate the effectiveness of the obtained results.

关键词： uncertain two-dimensional systems roesser model Lyapunov stability theory control synthesis

Output Feedback Robust H_(∞) Control for Discrete 2D Switched Systems

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Computer Systems Science & Engineering 2021年第10期39卷 69-85页

作者： Wenjun Gao Yang Yang Hongtao Duan Mingsheng Li Jinrong Ma Songwei Jin School of Electronic Information and Engineering Changchun University of Science and TechnologyChangchun130000China Department of Computer Science and Engineering University of CaliforniaRiversideCA92521USA

The two-dimensional(2-D)system has a wide range of applications in different fields,including satellite meteorological maps,process control,and digital ***,the research on the stability of 2-D systems is of great *** that multiple systems exist in switching and alternating work in the actual production process,but the system itself often has external perturbation and *** solve the above problems,this paper investigates the output feedback robust H_(∞)stabilization for a class of discrete-time 2-D switched systems,which the roesser model with uncertainties ***,sufficient conditions for exponential stability are derived via the average dwell time method,when the system’s interference and external input are ***,in the case of introducing the external interference,the weighted robust H_(∞)disturbance attenuation performance of the underlying system is further *** output feedback controller is then proposed to guarantee that the resulting closed-loop system is exponentially stable and has a prescribed disturbance attenuation levelγ.All theorems mentioned in the article will also be given in the form of linear matrix inequalities(LMI).Finally,a numerical example is given,which takes two uncertain values respectively and solves the output feedback controller’s parameters by the theorem proposed in the *** to the required controller parameter values,the validity of the theorem proposed in the article is compared and verified by simulation.

关键词： 2-D systems robust H_(∞)control LMI output feedback switched systems roesser model

Stabilization of Discrete-time 2-D T-S Fuzzy Systems Based on New Relaxed Conditions

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自动化学报 2010年第2期36卷 267-273页

作者： XIE Xiang-Peng ZHANG Hua-Guang Key Laboratory of Integrated Automation for the Process Industry Ministry of Education Shenyang 110004 P.R. China School of Information Science and Engineering Northeastern University Shenyang 110004 P.R. China

This paper is concerned with the problem of stabilization of the roesser type discrete-time nonlinear 2-D system that plays an important role in many practical applications. First, a discrete-time 2-D T-S fuzzy model is proposed to represent the underlying nonlinear 2-D system. Second, new quadratic stabilization conditions are proposed by applying relaxed quadratic stabilization technique for 2-D case. Third, for sake of further reducing conservatism, new non-quadratic stabilization conditions are also proposed by applying a new parameter-dependent Lyapunov function, matrix transformation technique, and relaxed technique for the underlying discrete-time 2-D T-S fuzzy system. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

关键词： roesser model 2-D discrete systems Takagi-Sugeno (T-S) fuzzy model relaxed stabilization conditions

Relaxed Stabilization Conditions for Discrete-Time 2-D T-S Fuzzy Systems

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Relaxed Stabilization Conditions for Discrete-Time 2-D T-S F...

2011 Chinese Control and Decision Conference（CCDC）

作者： Dawei Ding,Xiaoli Li and Dexin Liu are with the School of Automation and Electrical Engineering,and the Key Laboratory of Advanced Control of Iron and Steel Process (Ministry of Education),University of Science and Technology Beijing,Beijing 100083,China.Xiangpeng Xie is with the College of Information Science and Engineering,Northeastern University,Shenyang 110004,China.

This paper focuses on the problem of further relaxing stabilization conditions for the roesser type discretetime 2-D T-S fuzzy system.A novel kind of non-PDC control scheme is proposed to stabilize the closed-loop 2-D T-S fuzzy system,and then less conservative stabilization conditions are developed by using a new non-quadratic Lyapunov function for the underlying 2-D T-S fuzzy *** one fixed degree of the homogeneous polynomially parameter-dependent matrix,the conservatism could be further reduced by exploiting the algebraic property of fuzzy membership functions and the obtained stabilization conditions may asymptotically approach to exactness in a convergent ***,there are no slack matrix variables introduced in the control synthesis,and hence the computational burden is less than the existing ones while the same or less conservative results could be obtained.A numerical example is also provided to illustrate the effectiveness of the proposed methods.

关键词： roesser model 2-D discrete-time systems Stabilization LMI.

Structural Insights and Constructive Procedures for Multidimensional Realization and LFR Uncertainty modeling

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Structural Insights and Constructive Procedures for Multidim...

第二十六届中国控制会议

作者： Xu Li Dept.of Electronics and Information Systems Akita Prefectural University,Akita 015-0055,Japan

In this work,we review some new developments accomplished by the author and co-workers very recently for mul- tidimensional （nD） realization and LFR uncertainty *** particular,we shall show some substantial structural insights to this difficult problem that have not been clarified previously and new constructive procedures that can generate a low-order,possibly minimal roesser model realization for a rational or polynomial nD transfer matrix with numerical or/and symbolic *** will also be demonstrated by non-trivial examples that the proposed procedures are simple both conceptually and methodologically,and much more effective than the existing ones.

关键词： Multidimensional realization LFR uncertainty modeling roesser model Robust control

Finite-Frequency Fault Estimation of Two-Dimensional roesser Systems

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Finite-Frequency Fault Estimation of Two-Dimensional Roesser...

第32届中国控制与决策会议

作者： Xiaoxue Wu Heping Liu School of Automation and Electrical Engineering University of Science and Technology Beijing College of Science Liaoning Technical University

This paper is concerned with the fault estimation problem of a class of two-dimensional roesser systems subject to faults and disturbances in finite-frequency *** purpose of the paper is to design a fault estimation filter to detect the occurrence of faults and further estimate *** this end,two finite-frequency indices are used to describe the estimation *** conditions are derived via the generalized Kalman-Yakubovich-Popov（KYP） lemma,and an algorithm is developed to calculate the parameters of the desired *** examples have shown that the designed fault estimation filter can detect and estimate faults effectively.

关键词： two-dimensional systems roesser model fault estimation generalized KYP lemma fault detection