高维时滞动力系统的稳定性

基于多项式完全判别系统,该文讨论了高维时滞动力系统的全时滞稳定性、稳定性切换和区间稳定性,得到了简便实用的稳定性判据和检验方法.

含区间时变时滞系统的稳定性分析

研究了带有区间时变时滞系统的稳定性分析问题,并获得了一种新的判断区间时变时滞系统稳定的充分条件,引入新的Jensen积分不等式进行放缩,增加了适当的自由矩阵,减少了所获得结果的保守性,最后通过数值仿真例子验证了提出的方法的可行性和优越性.

对“不确定时滞系统的稳定条件”一文的评论及其修正

最近一篇论文 (杨开阳 ,井元伟 ,信息与控制 ,Vo130 ,№ 5 ,pp:4 74 - 4 76 ,2 0 0 1)利用比较原理 ,矩阵范数和矩阵测度的有关性质 ,提出了简单不确定时滞系统的稳定条件 .由于该文使用了一些不正确的条件 ,所以他们的结论是不可靠的 .本文指出了该文证明过程中的一些错误 ,并根据微分方程理论和矩阵指数特性 。

多重时滞不确定系统的鲁棒稳定判据

主要研究了一类具有范数有界不确定性的多重时滞不确定系统的鲁棒渐近稳定性分析问题．分别给出了多时滞不确定系统和单时滞不确定系统的时滞独立鲁棒稳定充分判据．此判据只利用了范数的概念，便于实用．

时滞微生物连续培养动力系统稳定性收敛速度的研究

讨论了具有时滞微生物连续培养动力系统的稳定性和α-稳定性.应用时滞系统稳定性切换几何判据法研究了系统的线性稳定性和α-稳定性,并比较这两个稳定性的区别与联系.最后应用数值模拟验证结论的准确性和有效性.

Improved delay-dependent stability criteria for stochastic systems with time-varying interval delay

The problem of the stability for a class of stochastic systems with time-varying interval delay and the norm-bounded uncertainty is investigated. Utilizing the information of both the lower and the upper bounds of the interval time-varying delay, a novel Lyapunov-Krasovskii functional is constructed. The delay-dependent sufficient criteria are derived in terms of linear matrix inequalities （LMIs）, which can be easily checked by the LMI in the Matlab toolbox. Based on the Jensen integral inequality, neither model transformations nor bounding techniques for cross terms is employed, so the derived criteria are less conservative than the existing results. Meanwhile, the computational complexity of the obtained stability conditions is reduced because no redundant matrix is introduced. A numerical example is given to show the effectiveness and the benefits of the proposed method.

Exponential Stability of Large-Scale Non-Linear Systems with Multiple The Delays

The problem of stabilizing a class of large-scale non-linear multiple delay systems is considered.The complicated system is decomposed into several subsystems; each function of them is expressed by a set of components of the overall state vector,with interconnections between them, and the subsystems are coupled by the delayed state. In this paper, a method is devised to be a suitable choice of state feedback controls of every subsystems, moreover, it is proved that the large-scale system is exponential stable.

On exponential stability for systems with state delays

This paper considers the issue of delay-dependent exponential stability for time-delay systems. Both nominal and uncertain systems are investigated. New sufficient conditions in terms of linear matrix inequalities(LMIs) are obtained. These criteria are simple owing to the use of an integral inequality. The model transformation approaches,bounding techniques for cross terms and slack matrices are all avoided in the derivation. Rigorous proof and numerical examples showed that the proposed criteria and those based on introducing slack matrices are equivalent.

Guaranteed cost control of uncertain system with input time-delay

For the uncertain continuous-time systems with input time-delay that widely exist in the production processes, we can get the existent conditions for the guaranteed cost control of these systems by using the Lyapunov stability theory, linear matrix inequalities theory and quadratic cost criterion. We can achieve the guaranteed cost control of this system by solving a matrix inequality. A state feed back guaranteed cost control law can be constructed by solving certain parameter-dependent Riccati matrix equation.

The Lotka-Volterra Competition System with Discrete and Distributed Time Delays

In this paper, the Lotka-Volterra competition system with discrete and distributed time delays is considered. By analyzing the characteristic equation of the linearized system, the local asymptotic stability of the positive equilibrium is investigated. Moreover, we discover the delays don＇t effect the stability of the equilibrium in the delay system. Finally, we can conclude that the positive equilibrium is global asymptotically stable in the delay system.

Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.

Guaranteed cost sampled-data control for uncertain nonlinear time-varying delay system

The robust guaranteed cost sampled-data control was studied for a class of uncertain nonlinear systems with time-varying delay. The parameter uncertainties are time-varying norm-bounded and appear in both the state and the input control matrices. By applying an input delay approach, the system was transformed into a continuous time-delay system. Attention was focused on the design of a robust guaranteed cost sampled-data control law which guarantees that the closed-loop system is asymptotically stable and the quadratic performance index is less than a certain bound for all admissible uncertainties. By applying Lyapunov stability theory, the theorems were derived to provide sufficient conditions for the existence of robust guaranteed cost sampled-data control law in the form of linear matrix inequalities (LMIs), especially an optimal state-feedback guaranteed cost sampled-data control law which ensures the minimization of the guaranteed cost was given. The effectiveness of the proposed method was illustrated by a simulation example with the asymptotically stable curves of system state under the initial condition of x(0)=[0.679 6 0].

A novel LMI criterion for power system stability with multiple time-delays

This paper presents a novel LMI criterion for electric power system stability with multiple time-delays.Initially,the linear time-invariant model of the power system with multiple delays is constructed,subsequently,the former criteria and the novel criterion of this paper are demonstrated in this paper,and the novel criterion is fully proved according to Lyapunov direct method.Specifically,the proposed criterion utilizes a properly simplified Lyapunov-Krasovskii functional,and no free-weighting matrix is introduced in the formation of new criterion,as a consequence,the calculation efficiency is remarkably enhanced.A typical second-order delay system,a single-generator-infinite-bus system and the WSCC 3-generator-9-bus delay system are taken to validate the effectiveness and efficiency enhancement of the proposed criterion.The numerical results indicate that the criterion of this paper can generate the same stability margin with the former ones.Further,the numerical results also verify that the proposed criterion’s efficiency is substantially boosted and calculation time is greatly curtailed.

STABILITY OF IMPULSIVE LINEAR HYBRID SYSTEMS WITH TIME DELAY

This paper investigates the stability of impulsive linear hybrid systems with time delay.And a number of delay-independent/delay-dependent stability criteria are obtained by using Lyapunovfunctions or Lyapunov functionals.Two examples are also presented to illustrate the effectiveness ofthe obtained results or to compare with the existing results.

NEW DELAY-DEPENDENT STABILITY CRITERIA AND ROBUST CONTROL OF NONLINEAR TIME-DELAY SYSTEMS

This paper investigates the stability analysis and H_∞ control for a class of nonlinear timedelay systems,and proposes a number of new results.Firstly,an equivalent form is given for this class of systems by means of coordinate transformation and orthogonal decomposition of vector fields.Then,based on the equivalent form,some delay-dependent results are derived for the stability analysis of the systems by constructing a novel Lyapunov functional.Thirdly,the authors use the equivalent form and the obtained stability results to investigate the H_∞ control problem for a class of nonhnear time-delay control systems,and present a control design procedure.Finally,an illustrative example is given to show the effectiveness of the results obtained in this paper.It is shown that the main results of this paper are easier to check than some existing ones,and have less conservatism.

L_2 DISTURBANCE ATTENUATION FOR A CLASS OF TIME-DELAY HAMILTONIAN SYSTEMS

This paper considers the problem of L2-disturbance attenuation for a class of time-delay port-controlled Hamiltonian systems. A v-dissipative inequality is established by using a proper control law and a storage function. Then based on the Razumikhin stability theorem, a sufficient condition is proposed for the asymptotically stability of the closed-loop system. Finally, the authors investigate the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain and an L2 disturbance attenuation control law is proposed. Study of illustrative example with simulation shows that the presented method in this paper works very well in the disturbance attenuation of time-delay Hamiltonian systems.

IMPROVED STABILITY CRITERIA FOR UNCERTAIN LINEAR SYSTEMS WITH INTERVAL TIME-VARYING DELAY

This paper deals with the robust stability analysis of dynamic systems with interval time- varying delay and uncertainties. The innovation of the method includes employment of a tighter integral inequality and construction of an appropriate type of Lyapunov functional. The stability criteria derived from this method have less conservatism than some existing ones. Numerical examples are given to illustrate the effectiveness of the orooosed method.

TWO EFFECTIVE STABILITY CRITERIA FOR LINEAR TIME-DELAY SYSTEMS WITH COMPLEX COEFFICIENTS

This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization （ETDAS） control and n time delay auto-synchronization （NTDAS） control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.

Projective Synchronization Between Two Nonidentical Variable Time Delayed Systems

In this paper, we propose a method for the projective synchronization between two different chaotic systems with variable time delays. Using active control approach, the suitable controller is constructed to make the states of two different diverse time delayed systems asymptotically synchronize up to the desired scaling factor. Based on the Lyapunov stability theory, the sufficient condition for the projective synchronization is calculated theoretically. Numerical simulations of the projective synchronization between Maekey-Glass system and Ikeda system with variable time delays are shown to validate the effectiveness of the proposed algorithm.

Robust Stability of Neutral Systems:A Discretized Lyapunov Functional Method

This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method.