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CONSENSUS AND r-CONSENSUS PROBLEMS FOR singular systems

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Journal of systems Science & Complexity 2014年第2期27卷 252-262页

作者： ZHANG Lequn FENG Jun-e YAO Juan School of Mathematics Shandong University

In this paper, the problem of consensus for continuous time singular systems of multi-agent networks is considered. The definition of r-consensus is introduced for singular systems of multi-agent networks. Firstly, linear systems with algebraic constraints are considered, and the corresponding results about consensus and average-consensus are derived. Then r-consensus and consensus problems of singular systems are investigated. Sufficient conditions of r-consensus and consensus are obtained,respectively. Finally, an illustrative example is given to show the effectiveness of the proposed method.

关键词： Balanced graphs consensus r-consensus singular systems strong connected graphs.

Modeling and analysis of singular systems via orthogonal triangular functions

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控制理论与应用（英文版） 2013年第2期11卷 141-148页

作者： Suchismita GHOSH Anish DEB Srimanti Roy CHOUDHURY Gautam SARKAR Department of Electrical Engineering MCKV Institute of Engineering Department of Applied Physics University of Calcutta92 APC RoadKolkata 700009 India Department of Electrical Engineering Budge Budge Institute of Technology Department of Applied Physics University of Calcutta2 APC RoadKolkata 700009 India

This paper presents a new approach to singular system analysis by modeling the system in terms of orthog- onal triangular functions （TFs）. The proposed method is more accurate compared to block pulse function-based analysis with respect to mean integral square error （MISE）. A numerical example involving four states of a singular system is treated and solutions obtained thereof. Four tables and relevant curves are presented to compare the respective coefficients in block pulse function （BPF） domain as well as in TF domain. The percentage error of the samples determined via TF domain are compared with the exact samples of the states. Furthermore, MISE for both BPF and TF analysis are computed and compared to reveal the efficiency of TF-based analysis.

关键词： singular systems Triangular functions Block pulse functions System analysis Modeling

REGULARIZATION OF singular systems BY OUTPUTFEEDBACK

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Journal of Computational Mathematics 2000年第1期18卷 43-60页

作者： De-lin Chu Da-yong Cai(Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China) 清华大学北京 100084

Presents a study which examined problem of regularization of a singular linear time-invariant system by derivative and proportional output feedback. Reduced form for the system that can be computed using orthogonal tr... 详细信息

关键词： regularization singular systems output feedback

Delay Dependent Robust Stability of singular systems with Additive Time-varying Delays

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International Journal of Automation and computing 2013年第1期10卷 85-90页

作者： N. Chaibi E. H. Tissir A. Hmamed Laboratory of Electronics Signals Systems and Data Processing (LESSI) Department of Physics Faculty of Sciences Dhar El Mahraz University Sidi Mohammed Ben Abellah

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities （LMIs）. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

关键词： singular systems additive time-varying delays linear matrix inequalities (LMIs) robust stability delay-dependent conditions

Absolute stabilization of singular systems with ferromagnetic hysteresis nonlinearity

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Science China(Information Sciences) 2013年第7期56卷 259-272页

作者： ZHANG HuaGuang WANG YingChun SONG Zheng School of Information Science and Engineering Northeastern University Stake Key Laboratory of Synthetical Automation of Process Industies (Northeasten University) Beijing Institute of Spacecraft System Engineering

This paper is concerned with the absolute stabilization problem of a class of singular systems with feedback connected ferromagnetic hysteresis nonlinearities. Firstly, a novel differential-integral loop transformation framework is developed to achieve an augmented singular system model. Secondly, by constructing a new passive output derivative operator of hysteresis nonlinearity and establishing the bound condition of the solution of ferromagnetic hysteresis model, the equivalent absolute stability criterion of singular systems with hysteresis feedback is derived based on KYP method and LMIs technique. Furthermore, the strict LMIs conditions for absolute stabilization are obtained, which can easily be checked by the LMI toolbox in MATLAB. Finally, two examples are given to illustrate the effectiveness of the proposed method.

关键词： ferromagnetic hysteresis singular systems absolute stability extended Popov criterion

A Stability Criterion for singular systems with Two Additive Time-varying Delay Components

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International Journal of Automation and computing 2013年第1期10卷 39-45页

作者： Jian-Min Jiao Department of Mathematics Baoji University of Arts and Sciences

The problem of stability for singular systems with two additive time-varying delay components is investigated. By constructing a simple type of Lyapunov-Krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms, a delay-dependent stability criterion is established for the considered systems to be regular, impulse free, and stable in terms of linear matrix inequalities （LMIs）. Based on this criterion, some new stability conditions for singular systems with a single delay in a range and regular systems with two additive time-varying delay components are proposed. These developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism. Finally, two numerical examples are employed to illustrate the effectiveness of the obtained theoretical results.

关键词： singular systems additive delay components stability Lyapunov-Krasovskii functional linear matrix inequality (LMI)

Robust L2-L∞ control for uncertain singular systems with time-varying delay

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Progress in Natural Science:Materials International 2008年第8期18卷 1015-1021页

作者： Lin Lia,*, Yingmin Jiaa, Junping Dub, Shiying Yuan c a The Seventh Research Division, Beijing University, Beijing 100083, China b Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia, Beijing University of Posts and Telecommunications, Beijing 100876, China c School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China The Seventh Research Division Beijing University Beijing 100083 China Beijing Key Laboratory of Intelligent Telecommunications Software and Multimedia Beijing University of Posts and Telecommunications Beijing 100876 China School of Electrical Engineering and Automation Henan Polytechnic University Jiaozuo 454000 China

We study the problem of L2-L1 control for a class of uncertain singular systems with time-delay and norm-bounded parameter uncertainties in this paper. A new delay-dependent robust stability criterion is obtained in terms of linear matrix inequalities (LMIs). Based on this criterion, a state feedback controller is designed to guarantee that the closed-loop system is regular, impulse free and stable with a prescribed L2-L1 performance satisfied for all admissible parameter uncertainties. A simulation example is included to illustrate the effectiveness of the proposed method.

关键词： L2–L1 control singular systems Delay-dependent condition LMIs

STRUCTURAL DECOMPOSITION AND ITS PROPERTIES OF LINEAR MULTIVARIABLE singular systems

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Journal of systems Science & Complexity 2007年第2期20卷 198-214页

作者： Minghua HE Ben M. CHEN Zongli LIN School of Electrical Engineering and Automation Fuzhou University Fuzhou 350002 China Department of Electrical and Computer Engineering The National University of Singapore Singapore 117576 Republic of Singapore. Charles L. Brown Department of Electrical and Computer Engineering University of Virginia Charlottesville VA 22904-4743 USA

We present in this paper a structural decomposition for linear multivariable singular systems. Such a decomposition has a distinct feature of capturing and displaying all the structural properties, such as the finite and infinite zero structures, invertibility structures, and redundant dynamics of the given system. As its counterpart for non-singular systems, we believe that the technique is a powerful tool in solving control problems for singular systems.

关键词： Descriptor systems singular systems structural invariants system decomposition

Robust H_∞ reliable control for uncertain singular systems with state delay

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Journal of systems Engineering and Electronics 2005年第3期16卷 640-644页

作者：向峥嵘陈庆伟胡维礼 Dept .of Automation Nanjing Univ .of Science and Technology

The problem of robust and H∞ reliable control for a class of uncertain singular systems with state time-delay is concerned. The problem we address is to design a state feedback controller such that the resulting close-loop systems is regular, impulse free and stable for all admissible uncertainties as well as actuator faults among a prespecified subset. A linear matrix inequality （LMI） design approach is proposed to solve the problem addressed with Hoo norm bound constraint on disturbance attenuation. Finally, a numerical example is provided to demonstrate the application of the proposed method.

关键词： singular systems delay systems parameter uncertainties reliable control linear matrix inequality (LMI) H∞ control.