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Switched Exponential State Estimation and Robust Stability for Interval Neural Networks with Discrete and Distributed Time Delays
Hongwen Xu,Huaiqin Wu,Ning Li
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/103542
Abstract: The interval exponential state estimation and robust exponential stability for the switched interval neural networks with discrete and distributed timedelays are considered. Firstly, by combining the theories of the switched systems and the interval neural networks, the mathematical model of the switched interval neural networks with discrete and distributed time delays and the interval estimation error system are established. Secondly, by applying the augmented Lyapunov-Krasovskii functional approach and available output measurements, the dynamics of estimation error system is proved to be globally exponentially stable for all admissible time delays. Both the existence conditions and the explicit characterization of desired estimator are derived in terms of linear matrix inequalities (LMIs). Moreover, a delay-dependent criterion is also developed, which guarantees the robust exponential stability of the switched interval neural networks with discrete and distributed time delays. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.
Robust Control for Uncertain Switched Systems with Interval Nondifferentiable Time-Varying Delays
T. La-inchua,P. Niamsup
Journal of Applied Mathematics , 2012, DOI: 10.1155/2012/718618
Abstract: This paper addresses the conditions for robust stabilization of a class of uncertain switched systems with delay. The system to be considered is autonomous and the state delay is time-varying. Using Lyapunov functional approach, restriction on the derivative of time-delay function is not required to design switching rule for the robust stabilization of switched systems with time-varying delays. The delay-dependent stability conditions are presented in terms of the solution of LMIs which can be solved by various available algorithms. A numerical example is given to illustrate the effectiveness of theoretical results.
Global Robust Stability of Switched Interval Neural Networks with Discrete and Distributed Time-Varying Delays of Neural Type
Huaiqin Wu,Ning Li,Kewang Wang,Guohua Xu,Qiangqiang Guo
Mathematical Problems in Engineering , 2012, DOI: 10.1155/2012/361871
Abstract: By combing the theories of the switched systems and the interval neural networks, the mathematics model of the switched interval neural networks with discrete and distributed time-varying delays of neural type is presented. A set of the interval parameter uncertainty neural networks with discrete and distributed time-varying delays of neural type are used as the individual subsystem, and an arbitrary switching rule is assumed to coordinate the switching between these networks. By applying the augmented Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI) techniques, a delay-dependent criterion is achieved to ensure to such switched interval neural networks to be globally asymptotically robustly stable in terms of LMIs. The unknown gain matrix is determined by solving this delay-dependent LMIs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.
Exponential Stability for a Class of Switched Nonlinear Systems with Mixed Time-Varying Delays via an Average Dwell-Time Method  [PDF]
N. Yotha,T. Botmart,T. Mouktonglang
ISRN Mathematical Analysis , 2012, DOI: 10.5402/2012/528259
Abstract: The problem of exponential stability for a class of switched nonlinear systems with discrete and distributed time-varying delays is studied. The constraint on the derivative of the time-varying delay is not required which allows the time delay to be a fast time-varying function. We study the stability properties of switched nonlinear systems consisting of both stable and unstable subsystems. Average dwell-time approached and improved piecewise Lyapunov functional combined with Leibniz-Newton are formulated. New delay-dependent sufficient conditions for the exponential stabilization of the switched systems are first established in terms of LMIs. A numerical example is also given to illustrate the effectiveness of the proposed method. 1. Introduction The switched systems are an important class of hybrid systems. They are described by a family of continuous or discrete-time subsystems and a rule that orchestrates the switching between the subsystems. Recently, switched systems have attracted much attention due to the widespread application in control, chemical engineering processing [1], communication networks, traffic control [2, 3], and control of manufacturing systems [4–6]. A switched nonlinear system with time delay is called switched nonlinear delay system, where delay may be contained in the system state, control input, or switching signals. In [7–9], some stability properties of switched linear delay systems composed of both stable and unstable subsystems have been studied by using an average dwell-time approach and piecewise Lyapunov functions. It is shown that when the average dwell time is sufficiently large and the total activation time of the unstable subsystems is relatively small compared with that of the Hurwitz stable subsystems, global exponential stability is guaranteed. The concept of dwell time was extended to average dwell time by Hespanha and Morse [10] with switching among stable subsystems. Furthermore, [11] generalized the results to the case where stable and unstable subsystems coexist. The stability analysis of nonlinear time-delay systems has received increasing attention. Time-delay systems are frequently encountered in various areas such as chemical engineering systems, biological modeling, and economics. The stability analysis for nonlinear time-delay systems has been investigated extensively. Various approaches to such problems have been proposed, see [12–14] and the references therein. It is well known that the existences of time delay in a system may cause instability and oscillations system. Thus, the stability analysis
A switching rule for exponential stability of switched recurrent neural networks with interval time-varying delay
Manlika Rajchakit, Grienggrai Rajchakit and Piyapong Niamsup
Advances in Difference Equations , 2013, DOI: 10.1186/1687-1847-2013-44
Abstract: This paper studies the problem for exponential stability of switched recurrent neural networks with interval time-varying delay. The time delay is a continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a set of argumented Lyapunov-Krasovskii functionals combined with Newton-Leibniz formula, a switching rule for exponential stability for of switched recurrent neural networks with interval time-varying delay is designed via linear matrix inequalities, and new sufficient conditions for the exponential stability of switched recurrent neural networks with interval time-varying delay via linear matrix inequalities(LMIs). A numerical example is given to illustrate the effectiveness of the obtained result.
Exponential Admissibility and Dynamic Output Feedback Control of Switched Singular Systems with Interval Time-Varying Delay  [PDF]
Jinxing Lin,Chunxia Fan
Mathematical Problems in Engineering , 2010, DOI: 10.1155/2010/680382
Abstract: This paper is concerned with the problems of exponential admissibility and dynamic output feedback (DOF) control for a class of continuous-time switched singular systems with interval time-varying delay. A full-order, dynamic, synchronously switched DOF controller is considered. First, by using the average dwell time approach, a delay-range-dependent exponential admissibility criterion for the unforced switched singular time-delay system is established in terms of linear matrix inequalities (LMIs). Then, based on this criterion, a sufficient condition on the existence of a desired DOF controller, which guarantees that the closed-loop system is regular, impulse free and exponentially stable, is proposed by employing the LMI technique. Finally, some illustrative examples are given to show the effectiveness of the proposed approach. 1. Introduction The past decades have witnessed an enormous interest in switched systems, due to their powerful ability in modeling of event-driven systems, logic-based systems, parameter- or structure-varying systems, and so forth; for details, see [1–4] and the references therein. Switched systems are a class of hybrid systems, which consist of a collection of continuous- or discrete-time subsystems and a switching rule specifying the switching between them. When focusing on the classification problems in switched systems, it is commonly recognized that there exist three basic problems [1]: (i) finding conditions for stability under arbitrary switching; (ii) identifing the limited but useful class of stabilizing switching signals, and (iii) construct a stabilizing switching signal. Many effective methods have been presented to tackle these three basic problems such as the multiple Lyapunov function approach [5], the piecewise Lyapunov function approach [6], the switched Lyapunov function approach [7], the convex combination technique [8], and the dwell time or average dwell time scheme [9–12]. On the other hand, time-delay is very common in engineering systems and is frequently a source of instability and poor performance [13]. Therefore, control of switched time-delay systems has received more and more attention in the past few years; see [14–23] and the references therein. As far as we know, singular systems (known also as descriptor, implicit or differential algebraic systems) also provide a natural framework for modeling of dynamic systems and describe a larger class of systems than the regular system models [24]. Switched singular systems have strong engineering background such as electrical networks [25], economic
Exponential Stabilization of Neutral-Type Neural Networks with Interval Nondifferentiable and Distributed Time-Varying Delays
W. Weera,P. Niamsup
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/101426
Abstract: The problem of exponential stabilization of neutral-type neural networkswith various activation functions and interval nondifferentiable and distributed time-varyingdelays is considered. The interval time-varying delay function is not requiredto be differentiable. By employing new and improved Lyapunov-Krasovskii functionalcombined with Leibniz-Newton’s formula, the stabilizability criteria are formulated interms of a linear matrix inequalities. Numerical examples are given to illustrate and show theeffectiveness of the obtained results.
Global robust exponential stability of interval cellular neural networks with time-varying delays
区间时变细胞神经网络的全局鲁棒指数稳定性

WU Li-gang,WANG Chang-hong,ZENG Qing-shuang,
吴立刚
,王常虹,曾庆双

控制理论与应用 , 2006,
Abstract: The global robust exponential stability (GRES) of a class of interval cellular neural networks with time-varying delays is studied in this paper. A transformation is made on original system by the Leibniz-Newton formula, an analysis is also given to show that those two systems are equivalent. Based on the transformed model, applying Lyapunov-Krasovskii stability theorem for functional differential equations and the linear matrix inequality (LMI) approach, some delay-dependent criteria are respectively presented for the existence, uniqueness, and global robust exponential stability of the equilibrium for the interval delayed neural networks. The criteria given here are less conservative than those provided in the earlier references. Finally, numerical example is included to demonstrate the effectiveness and superiority of the proposed results.
Reliable L 1 control of positive switched systems with time-varying delays
Mei Xiang and Zhengrong Xiang
Advances in Difference Equations , 2013, DOI: 10.1186/1687-1847-2013-25
Abstract: This paper deals with the reliable control problem of positive switched systems with time-varying delays. Under the case where both stable and unstable subsystems coexist, sufficient conditions are proposed to guarantee the exponential stability of positive switched systems with time-varying delays, and the average dwell time approach is utilized for the stability analysis. The result is also extended to solve the reliable control problem. All the results are formulated in a set of linear matrix inequalities (LMIs), which can be easily verified or implemented. The obtained theoretical results are demonstrated by a numerical example.
Mean-Square Exponential Synchronization of Markovian Switching Stochastic Complex Networks with Time-Varying Delays by Pinning Control
Jingyi Wang,Chen Xu,Jianwen Feng,Man Kam Kwong,Francis Austin
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/298095
Abstract: This paper investigates the mean-square exponential synchronization of stochastic complex networks with Markovian switching and time-varying delays by using the pinning control method. The switching parameters are modeled by a continuous-time, finite-state Markov chain, and the complex network is subject to noise perturbations, Markovian switching, and internal and outer time-varying delays. Sufficient conditions for mean-square exponential synchronization are obtained by using the Lyapunov-Krasovskii functional, Itö’s formula, and the linear matrix inequality (LMI), and numerical examples are given to demonstrate the validity of the theoretical results.
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