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IEEE/CAA Journal of Automatica Sinica 2021年第1期8卷 77-85页

作者： Xian-Ming Zhang Qing-Long Han Xiaohua Ge the School of Software and Electrical Engineering Swinburne University of TechnologyMelbourneVIC 3122Australia

One of challenging issues on stability analysis of time-delay systems is how to obtain a stability criterion from a matrix-valued polynomial on a time-varying delay.The first contribution of this paper is to establish a necessary and sufficient condition on a matrix-valued polynomial inequality over a certain closed interval.The degree of such a matrix-valued polynomial can be an arbitrary finite positive integer.The second contribution of this paper is to introduce a novel LyapunovKrasovskii functional,which includes a cubic polynomial on a time-varying delay,in stability analysis of time-delay systems.Based on the novel Lyapunov-Krasovskii functional and the necessary and sufficient condition on matrix-valued polynomial inequalities,two stability criteria are derived for two cases of the time-varying delay.A well-studied numerical example is given to show that the proposed stability criteria are of less conservativeness than some existing ones.

关键词： Bessel-Legendre inequality matrix-valued polynomial inequalities stability time-varying delay time-delay systems

Robust Leader-Following Output Regulation of Uncertain Multi-Agent Systems With time-varying delay

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IEEE/CAA Journal of Automatica Sinica 2018年第4期5卷 807-817页

作者： Ala Shariati Qing Zhao Automation&Control Research Group Faculty of Electrical and Computer EngineeringKhajeh Nasir Toosi University of TechnologyTehran ***Iran Department of Electrical and Computer Engineering at University of Alberta EdmontonAlberta T6R1Z6Canada

In this paper, the robust analysis and design of leader-following output regulation for multi-agent systems described by general linear models is given in presence of timevarying delay and model uncertainty. To this aim, a new regulation protocol for the closed-loop multi-agent system under a directed graph is proposed. An important specification of the proposed protocol is to guarantee the leader-following output regulation for uncertain multi-agent systems with both stable and unstable agents. Since many signals can be approximated by a combination of the stationary and ramp signals, the presented results work for adequate variety of the leaders. The analysis and design conditions are presented in terms of certain matrix inequalities. The method proposed can be used for both stationary and ramp leaders. Simulation results are presented to show the effectiveness of the proposed method.

关键词： Linear matrix inequality(LMI) multi-agent systems robust leader-following output regulation time-varying delay

Robust Finite-time H_∞ Control of Linear time-varying delay Systems with Bounded Control via Riccati Equations

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International Journal of Automation and computing 2018年第3期15卷 355-363页

作者： Piyapong Niamsup Vu N.Phat Department of Mathematics Faculty of Science Chiang Mai University Institute of Mathematics VAST

In this paper, we will present new results on robust finite-time H∞ control for linear time-varying systems with both time-varying delay and bounded control. delay-dependent sufficient conditions for robust finite-time stabilization and H∞ control are first established to guarantee finite-time stability of the closed-loop system via solving Riccati differential equations. Applications to finite-time H∞ control to a class of linear autonomous time-delay systems with bounded control are also discussed in this paper.Numerical examples are given to illustrate the effectiveness of the proposed method.

关键词： Finite-time stability H∞ control bounded control time-varying delay Riccati equation.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A time-varying delay IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

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Acta Mathematica Scientia 2017年第5期37卷 1453-1471页

作者： Vamna BOUKHATEM Benyattou BENABDERRAHMANE Laboratory of Pure and Applied Mathematics University of LaghouatP.O.Box 37GLaghouat 03000Algeria Laboratory of Pure and Applied Mathematics Mohamed Boudiaf UniversityM'sila 28000Algeria

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

关键词： acoustic boundary conditions general decay time-varying delay variable coefficients viscoelastic equation

Static output feedback stabilization for systems with time-varying delay based on a matrix transformation method

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Science China(Information Sciences) 2015年第1期58卷 188-200页

作者： LIU Zhen Wei ZHANG HuaGuang SUN QiuYe College of Information Science and Engineering Northeastern University State Key Laboratory of Synthetical Automation for Process Industries Northeastern University

This paper is concerned with the problem of static output feedback stabilization for linear systems with time-varying delay. A novel controller design is proposed based on a matrix transformation method with a new equation condition, which can solve the controller gain more easily and avoid complicated calculations of the non-linear matrix inequality. Then, the corresponding criteria can be obtained by combining the matrix transformation method and the ideas of non-uniformly dividing delay interval, which can guarantee the asymptotic stability of the closed-loop systems and calculate the satisfactory controller gain. Finally, two numerical examples are provided to verify the effectiveness of the proposed design scheme.

关键词： static output feedback matrix transformation method time-varying delay non-uniformly dividing delay interval equation condition

Fault detection and optimization for networked control systems with uncertain time-varying delay

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Journal of Systems Engineering and Electronics 2015年第3期26卷 544-556页

作者： Qing Wang Zhaolei Wang Chaoyang Dong Erzhuo Niu School of Automation Science and Electrical Engineering Beihang University Beijing Aerospace Automatic Control Institute School of Aeronautic Science and Engineering Beihang University Flight Automatic Control Research Institute Aviation Industry Corporation

The observer-based robust fault detection filter design and optimization for networked control systems （NOSs） with uncer- tain time-varying delays are addressed. The NCSs with uncertain time-varying delays are modeled as parameter-uncertain systems by the matrix theory. Based on the model, an observer-based residual generator is constructed and the sufficient condition for the existence of the desired fault detection filter is derived in terms of the linear matrix inequality. Furthermore, a time domain opti- mization approach is proposed to improve the performance of the fault detection system. To prevent the false alarms, a new thresh- old function is established, and the solution of the optimization problem is given by using the singular value decomposition （SVD） of the matrix. A numerical example is provided to illustrate the effectiveness of the proposed approach.

关键词： fault detection networked control systems residual generator time-varying delay time domain optimization approach.

Exponential synchronization of chaotic Lur'e systems with time-varying delay via sampled-data control

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Chinese Physics B 2014年第6期23卷 104-117页

作者： R.Rakkiyappan R.Sivasamy S.Lakshmanan Department of Mathematics Bharathiar University Department of Mathematics College of Science UAE University

In this paper, we study the exponential synchronization of chaotic Lur＇e systems with time-varying delays via sampled-data control by using sector nonlinearties. In order to make full use of information about sampling intervals and interval time-varying delays, new Lyapunov-Krasovskii functionals with triple integral terms are introduced. Based on the convex combination technique, two kinds of synchronization criteria are derived in terms of linear matrix inequal- ities, which can be efficiently solved via standard numerical software. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed results.

关键词： exponential synchronization chaotic Lur＇e system time-varying delay sampled-data control

New criteria on delayed state feedback stabilization for stochastic systems with time-varying delay

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Journal of Systems Engineering and Electronics 2013年第3期24卷 519-527页

作者： Shiguo Peng School of Automation Guangdong University of Technology

The problems of robust exponential stability in mean square and delayed state feedback stabilization for uncertain stochastic systems with time-varying delay are studied. By using Jensen＇s integral inequality and combining with the free weighting matrix approach, new delay-dependent stability conditions and delayed state feedback stabilization criteria are obtained in terms of linear matrix inequalities. Meanwhile, the proposed delayed state feedback stabilization criteria are more convenient in application than the existing ones since fewer tuning parameters are involved. Numerical examples are given to illustrate the effectiveness of the proposed methods.

关键词： stochastic system time-varying delay delay-depen- dent exponential stability delayed state feedback stabilization.

Stability of nonlinearly-perturbed systems with time varying delay using LMIs

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Journal of Systems Engineering and Electronics 2013年第6期24卷 1011-1018页

作者： S.Jeeva Sathya Theesar P.Balasubramaniam Institute for Mathematical Sciences University of Malaya Department of Mathematics Gandhigram Rural Institute-Deemed University

This paper studies delay dependent robust stability and the stabilization problem of nonlinear perturbed systems with time varying delay. A new set of sufficient conditions for the stability of open as well as close loop systems are obtained in the sense of Lyapunov-Krasovskii. To reduce the conservatism, the work exploits the idea of splitting the delay interval into multiple equal regions so that less information on the time delay can be imposed to derive the results. The derived criterion not only improves the upper bounds of the time delay but also does not require the derivative of the delay to be known at prior. Easily testable sufficient criteria are presented in terms of linear matrix inequalities. It is shown that the derived conditions are very less conservative while comparing the maximum allowable upper bound of delay with the existing results in literature.

关键词： delay dependent stability time-varying delay nonlinear perturbations

Non-fragile robust H_(∞)control of nonlinear networked control systems with time-varying delay and unknown actuator failures

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International Journal of Intelligent Computing and Cybernetics 2016年第3期9卷 298-312页

作者： Yueming Zhi Shun Jiang Feng Pan Jiangnan University WuxiChina Department of Automation Jiangnan UniversityWuxiChina

Purpose-This paper is concerned with non-fragile robust H_(∞)control problems for nonlinear networked control systems(NCSs)with time-varying delay and unknown actuator failures.The paper aims to discuss these issues.Design/methodology/approach-The system parameters are allowed to have time-varying uncertainties and the actuator faults are unknown but whose upper and lower bounds are known.By using some lemmas,uncertainties can be replaces with the known values.By taking the exogenous disturbance and network transmission delay into consideration,a delay nonlinear system model is constructed.Findings-Based on Lyapunov stability theory,linear matrix inequalities(LMIs)and free weighting matrix methods,the sufficient conditions for the existence of the non-fragile robust H_(∞)controller gain are derived and which can obtained by solving the LMIs.Finally,a numerical example is provided to illustrate the effectiveness of the proposed methods.Originality/value-The introduced approach is interesting for NCSs with time-varying delay and unknown actuator failures.

关键词： time-varying delay LMIs Nonlinear NCSs Robust H_(∞)control Unknown actuator failure