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1.
The exponential stability problem is investigated for a class of uncertain stochastic neural networks with discrete and unbounded distributed time delays. Two types of uncertainty are considered: one is time‐varying structured uncertainty, whereas the other is interval uncertainty. With the application of the Jensen integral inequality and constructing appropriate Lyapunov–Krasovskii functional based on delay partitioning, several improved delay‐dependent criteria are developed to achieve the exponential stability in mean square in terms of linear matrix inequalities. It is established theoretically that two special cases of the obtained criteria are less conservative than some existing results but including fewer slack variables. As the present conditions involve fewer free weighting matrices, the computational burden is largely reduced. Three numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
2.
Keqin Gu 《国际强度与非线性控制杂志
》2003,13(11):1017-1033
》2003,13(11):1017-1033
The previously proposed discretized Lyapunov functional method for systems with multiple delay is refined using variable elimination and Jensen inequality. The resulting new stability criterion is simpler. Numerical examples indicate that the new method is much less conservative for a given discretization mesh. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
3.
Stability of linear continuous‐time difference equations with distributed delay: Constructive exponential estimates 
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下载免费PDF全文 This paper is concerned with the construction of exponential estimates for a class of systems governed by continuous‐time difference equations with distributed delay. With the Lyapunov–Krasovskii approach, we propose sufficient conditions for exponential stability, with numerical constructive estimates. A conservatism analysis is made to illustrate the improvement of these stability conditions with respect to conditions already presented in the literature. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
4.
Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov–Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives. 相似文献
5.
Exponential estimates and sufficient conditions for the exponential stability of linear neutral time delay for systems with multiple delays are given. The case of systems with uncertainties, including uncertainties in the difference operator, is considered. The proofs follows from new results on non‐homogeneous difference equations evolving in continuous time combined with the Lyapunov–Krasovskii functionals approach. The conditions are expressed in terms of linear matrix inequalities. The particular case of neutral time delay systems with commensurate delays, which leads to less restrictive exponential estimates, is also addressed. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
6.
This paper addresses the problem of stability for a class of switched positive linear time‐delay systems. As first attempt, the Lyapunov–Krasovskii functional is extended to the multiple co‐positive type Lyapunov–Krasovskii functional for the stability analysis of the switched positive linear systems with constant time delay. A sufficient stability criterion is proposed for the underlying system under average dwell time switching. Subsequently, the stability result for system under arbitrary switching is presented by reducing multiple co‐positive type Lyapunov–Krasovskii functional to the common co‐positive type Lyapunov–Krasovskii functional. A numerical example is given to show the potential of the proposed techniques. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
7.
Exponential stability necessary conditions for linear periodic time‐delay systems are presented. They are obtained with the help of new properties of the Lyapunov matrix in the framework of Lyapunov–Krasvoskii functionals of complete type. An academic example illustrates our results. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
Saul Puga Moises Bonilla Michel Malabre Sabine Mondié Rogelio Lozano 《国际强度与非线性控制杂志
》2016,26(7):1395-1421
》2016,26(7):1395-1421
This paper proposes a control scheme for the problem of stabilizing partly unknown multiple‐input multiple‐output linear time‐varying retarded systems. The control scheme is composed by a singularly perturbed controller and a reference model. We assume the knowledge of a number of structural characteristics of the system as the boundedness and the knowledge of the bounds for the unknown parameters (and their derivatives) that define the system matrices, as well as the structure of these matrices. The results presented here are a generalization of previous results on linear time‐varying Single‐Input Single‐Output (SISO) and multiple‐input multiple‐output systems without delays and linear time‐varying retarded SISO systems. The closed‐loop system is a linear singularly perturbed retarded system with uniform asymptotic stability behavior. The uniform asymptotic stability of the singularly perturbed retarded system is guaranteed. We show how to design a control law such that the system dynamics for each output is given by a Hurwitz polynomial with constant coefficients. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
9.
This paper proposes an improvement to the delay‐dependent stability of discrete systems with time‐varying delays. The approach is based on the observation that the positive definiteness of a chosen Lyapunov–Krasovskii functional does not necessarily require all the involved symmetric matrices to be positive definite, which has been overlooked in the literature. The derived delay‐dependent stability conditions are in terms of linear matrix inequalities. It is theoretically proved that our results are less conservative than the corresponding ones obtained by requiring the positive definiteness of all the symmetric matrices in a chosen Lyapunov–Krasovskii functional. The importance of the present approach is that a great number of delay‐dependent analysis and synthesis results obtained by the aforementioned requirement in the literature can be improved by the present approach without introducing any new decision variables. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
10.
The problem of the stability of a linear system with an interval time‐varying delay is investigated. A new Lyapunov–Krasovskii functional that fully uses information about the lower bound of the time‐varying delay is constructed to derive new stability criteria. It is proved that the proposed Lyapunov–Krasovskii functional can lead to less conservative results than some existing ones. Based on the proposed Lyapunov–Krasovskii functional, two stability conditions are developed using two different methods to estimate Lyapunov–Krasovskii functional's derivative. Two numerical examples are given to illustrate that the two stability conditions are complementary and yield a larger maximum upper bound of the time‐varying delay than some existing results. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
11.
This paper is devoted to the evaluation of sampling interval providing robust exponential stability of nonlinear system with sector‐bounded nonlinearities. It extends our previous results (R. E. Seifullaev, A. L. Fradkov. Sampled‐data control of nonlinear oscillations based on LMIs and Fridman's method. In 5th IFAC International Workshop on Periodic Control Systems, 95‐100. Caen, France. 2013). The proposed approach exploits E. Fridman's method for linear systems based on a general time‐dependent Lyapunov–Krasovskii functional. With classical results of V. A. Yakubovich about S‐procedure, the problem is reduced to feasibility analysis of linear matrix inequalities. The results are illustrated by example: the pendulum system with friction and sector‐bounded multiple nonlinearities. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
12.
This paper deals with the state feedback controller design for a class of high‐order feedforward (upper‐triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher‐order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time‐delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
13.
In this paper we consider a special class of integral delay systems arising in several stability problems of time‐delay systems. For these integral systems we derive stability and robust stability conditions in terms of Lyapunov–Krasovskii functionals. More explicitly, after providing the stability conditions we compute quadratic functionals and apply them to derive exponential estimates for solutions, and robust stability conditions for perturbed integral delay systems. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
14.
In this paper, robust stability of uncertain linear neutral systems is analysed via a Lyapunov–Krasovskii constructive approach. This paper is the first attempt to compute the Lyapunov–Krasovskii functional for a given time derivative functional w(·) for the class of linear neutral type time delay systems. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
15.
A new method is proposed to determine the ultimate bounds and the convergence rates for perturbed time‐delay systems when the Lyapunov–Krasovskii functionals and their derivatives are available. Compared with existing methods, the proposed method is more concise, more widely applicable, and the obtained results are less conservative. To show the three features, the proposed method is applied to improve three existing results, respectively. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
16.
This paper discusses the problem of output feedback stabilization for a more general class of stochastic high‐order nonlinear systems with time‐varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed‐loop system is globally asymptotically stable in probability, by choosing an appropriate Lyapunov–Krasovskii functional. An example is given to illustrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
17.
This paper suggests a generalized zero equality lemma for summations, which leads to making a new Lyapunov–Krasovskii functional with more state terms in the summands and thus applying various zero equalities for deriving stability criteria of discrete‐time systems with interval time‐varying delays. Also, using a discrete‐time counter part of Wirtinger‐based integral inequality, Jensen inequality, and a lower bound lemma for reciprocal convexity, the forward difference of the Lyapunov–Krasovskii functional is bounded by the combinations of various state terms including not only summation terms but also their interval‐normalized versions, which contributes to making the criteria less conservative. Numerical examples show the improved performance of the criteria in terms of maximum delay bounds. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
This paper presents a new insight into the delay‐dependent stability for time‐delay systems. Because of the key observation that the positive definiteness of a chosen Lyapunov–Krasovskii functional does not necessarily require all the involved symmetric matrices in the Lyapunov–Krasovskii functional to be positive definite, an improved delay‐dependent asymptotic stability condition is presented in terms of a set of LMIs. This fact has been overlooked in the development of previous stability results. The importance of the present method is that a vast number of existing delay‐dependent results on analysis and synthesis of time‐delay systems derived by the Lyapunov–Krasovskii stability theorem can be improved by using this observation without introducing additional variables. The reduction of conservatism of the proposed result is both theoretically and numerically demonstrated. It is believed that the proposed method provides a new direction to improve delay‐dependent results on time‐delay systems. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
19.
This paper is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the new Lyapunov–Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some numerical examples and comparisons are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing results in the literature. Furthermore, the supplementary requirement that the time derivative of discrete time-varying delays must be smaller than the value one is not necessary to derive the results in this paper. 相似文献
20.
Jenq‐Der Chen 《国际强度与非线性控制杂志
》2007,17(12):1068-1087
》2007,17(12):1068-1087
In this paper, the problem of designing robust guaranteed cost control law for a class of uncertain neutral system with a given quadratic cost function is considered. Based on Lyapunov–Krasovskii functional theory, a delay‐dependent criterion for the existence of guaranteed cost controller is expressed in the form of two linear matrix inequalities (LMIs), which can be solved by using effective LMI toolbox. Moreover, a convex optimization problem satisfying some LMI constraints is formulated to solve a guaranteed cost controller which achieves the minimization of the closed‐loop guaranteed cost. An efficient approach is proposed to design the guaranteed cost control for uncertain neutral systems. Computer software Matlab can be used to solve all the proposed results. Finally, a numerical example is illustrated to show the usefulness of our obtained design method. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献