Delay Decomposition Approach Research Articles

Delay decomposition approach to state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters

This paper investigates the state estimation of neural networks with mixed time‐varying delays and Markovian jumping parameters. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. On the basis of the new Lyapunov–Krasovskii functional, some inequality techniques, stochastic stability theory and delay‐dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the less conservative and effectiveness of our theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Delay‐Range‐Dependent Stability Criteria for Takagi‐Sugeno Fuzzy Systems with Fast Time‐Varying Delays

The problem of delay‐range‐dependent stability for T‐S fuzzy system with interval time‐varying delay is investigated. 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. By developing delay decomposition approach, integral inequalities approach (IIA), and Leibniz‐Newton formula, the information of the delayed plant states can be taken into full consideration, and new delay‐dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Simulation examples show resulting criteria outperform all existing ones in the literature. It is worth pointing out that our criteria are carried out more efficiently for computation and less conservatism of the proposed criteria.

Mean-square exponential stability for stochastic time-varying delay systems with Markovian jumping parameters: A delay decomposition approach

Mean-square exponential stability for stochastic time-varying delay systems with Markovian jumping parameters: A delay decomposition approach

Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach

This paper is concerned with the problem of asymptotic stability of neutral systems. A new delay-dependent stability condition is derived in terms of linear matrix inequality to ensure a large upper bound of the time-delay by non-uniformly dividing the delay interval into multiple segments. A new Lyapunov–Krasovskii functional is constructed with different weighting matrices corresponding to different segments in the Lyapunov–Krasovskii functional, where both constant time delays and time-varying delays have been taken into account. Numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed methods.

New results of robust stability analysis for neutral-type neural networks with time-varying delays and Markovian jumping parameters1The work of authors was supported by Department of Science and Technology, New Delhi, India, under the sanctioned No. SR/S4/MS:485/07.

In this paper, robust stability analysis for neutral-type neural networks with time-varying delays and Markovian jumping parameters is conducted. By using the delay-decomposition approach, a new Lyapunov–Krasovskii functional is constructed. Based on this Lyapunov–Krasovskii functional and some stochastic stability theory, delay-dependent stability criteria are obtained in terms of linear matrix inequalities. Finally, three numerical examples are given to illustrate the effectiveness and reduced conservatism of our theoretical results.

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

This paper studies the problem of linear matrix inequality (LMI) approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov—Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay

This paper is concerned with delay-dependent passivity analysis for interval neural networks with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, new Lyapunov–Krasovskii functionals (LKFs) are constructed on these intervals. Employing these new LKFs, a new passivity criterion is proposed in terms of linear matrix inequalities, which is dependent on the size of the time delay. Finally, some numerical examples are given to illustrate the effectiveness of the developed techniques.

A delay decomposition approach to [formula omitted] filter design for stochastic systems with time-varying delay

This paper investigates the problem of L 2 – L ∞ filter design for a class of stochastic systems with time-varying delay. The addressed problem is the design of a full order linear filter such that the error system is asymptotically mean-square stable and a prescribed L 2 – L ∞ performance is satisfied. In order to develop a less conservative filter design, a new Lyapunov-Krasovskii functional (LKF) is constructed by decomposing the delay interval into multiple equidistant subintervals, and a new integral inequality is established in the stochastic setting. Then, based on the LKF and integral inequality, the delay-dependent conditions for the existence of L 2 – L ∞ filters are obtained in terms of linear matrix inequalities (LMIs). The resulting filters can ensure that the error system is asymptotically mean-square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Exponential stabilization of uncertain time-delay linear systems with Markovian jumping parameters

This paper studies the exponential stabilization problem of uncertain time-delay linear systems with Markovian jumping parameters. A novel delay decomposition approach is developed to derive delay-dependent conditions under which the closed-loop control system is mean square exponentially stable for all admissible uncertainties. It is shown that the feedback gain matrices and the decay rate can be obtained by solving coupled linear matrix inequalities. Moreover, the difficulties arising from searching for tuning parameters in the existing methods are overcome. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Master–slave synchronization criteria for horizontal platform systems using time delay feedback control

This paper is concerned with master–slave synchronization for two identical non-autonomous horizontal platform systems by using time-delay feedback control. Compared with some existing results on synchronization for horizontal platform systems, the effect of the time delay in the feedback control on master–slave synchronization is investigated. Applying a delay decomposition approach, some delay-dependent synchronization criteria are established and formulated in the form of linear matrix inequalities (LMIs). Sufficient conditions about the existence of a time delay feedback controller are derived by employing these newly obtained synchronization criteria. The controller gains can be achieved by solving a set of LMIs. One simulation example is given to illustrate the effectiveness of synchronization criteria and the design method.

Leakage Delays in T–S Fuzzy Cellular Neural Networks

In this paper, the Takagi---Sugeno (T---S) fuzzy model representation is extended to the stability analysis for cellular neural networks (CNNs) with mixed time-varying delays and time delay in the leakage term via the delay decomposition approach. First, a sufficient condition is given to ensure the existence and uniqueness of equilibrium point by using topological degree theory. Then, we present global asymptotic stability of equilibrium point by using linear matrix inequality (LMI) approach and by constructing an augmented Lyapunov---Krasovskii functional (ALKF) together with convex combination method. The proposed results can be easily solved by some standard numerical packages. Finally, four numerical examples are given to demonstrate the effectiveness and conservativeness of our proposed results.

Improved exponential stability criteria and stabilisation of T-S model-based neutral systems

This study deals with the β-exponential stability and stabilisation problems for a class of T-S model-based neutral systems. To solve these problems, new Lyapunov–Krasovskii functional candidates for this class of systems can be chosen by using the delay-decomposition approach and introducing some exponential functions into corresponding integrands. β-exponential stability conditions of the T–S model-based neutral systems are established by using the Lyapunov–Krasovskii functional and a modification integral inequality. An LMI-based state feedback controller design strategy for this class of systems is proposed based on one of the β-exponential stability conditions. Two numerical examples are also provided to illustrate the effectiveness of the proposed approach.

Delay decomposition approach to delay-dependent stability for singular time-delay systems

This study deals with the problem of delay-dependent stability analysis for singular time-delay systems. By employing the delay decomposition approach, an improved delay-dependent stability criterion is established in terms of linear matrix inequalities (LMIs), which ensures that the singular time-delay system is regular, impulse free and asymptotically stable. This stability criterion, which is obtained without using model transformation and bounding technique for cross-product terms, is much less conservative and includes some existing results as its special cases. Numerical examples are given to illustrate the effectiveness of the proposed method.

EFFECTS OF COUPLING DELAYS ON SYNCHRONIZATION IN LUR'E COMPLEX DYNAMICAL NETWORKS

This paper investigates the effects of coupling delays on synchronization in Lur'e complex dynamical networks. Every identical node in the network can be represented as a Lur'e system. Based on Lyapunov–Krasovskii functionals and Lur'e–Postnikov Lyapunov functionals, some delay-dependant synchronization criteria are derived by employing a delay decomposition approach. A Lur'e complex dynamical network with Chua's circuit nodes and one numerical example are given to illustrate the effectiveness of the synchronization criteria.

A delay decomposition approach to fuzzy Markovian jumping genetic regulatory networks with time-varying delays

In this paper, we investigated the asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach. The genetic regulatory networks are composed of s modes and the network switches from one mode to another according to a Markovian chain with known transition probabilities. Purpose of this work is to establish some easy-to-verify conditions under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov–Krasovskii functional (LKF) is constructed by nonuniformly dividing the whole delay intervals into multiple segments. Choosing proper functionals with different weighting matrices corresponding to different segments in the LKFs. Employing these new LKFs for the case of constant time delays and time-varying delays, some new delay-dependent stability criteria are established with Markovian jumping parameters by T–S fuzzy model. Maximum admissible upper bounds (MAUBs) for the time-varying delays are determined. All the conditions presented here are in the form of linear matrix inequalities (LMI) which are efficiently solved by the LMI toolbox in Matlab. Numerical examples are given to show the effectiveness of the proposed method.

Delay decomposition approach to stability analysis for uncertain fuzzy Hopfield neural networks with time-varying delay

This paper is concerned with delay-dependent stability analysis for uncertain Tagaki–Sugeno (T-S) fuzzy Hopfield neural networks (UFHNNs) with time-varying delay. By decomposing the delay interval into multiple equidistant subintervals, Lyapunov–Krasovskii functionals (LKFs) are constructed on these intervals. Employing these LKFs, a new stability criterion is proposed in terms of Linear Matrix Inequalities (LMIs), which is dependent on the size of the time delay and can be easily verified by MATLAB LMI toolbox. Numerical examples are given to illustrative the effectiveness of the proposed method.

Exponential convergence rate estimation for neutral BAM neural networks with mixed time-delays

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory neural networks with mixed time-delays, where discrete, distributed and neutral delays are involved. By utilizing the delay decomposition approach and an appropriately constructed Lyapunov–Krasovskii functional, some novel delay-dependent and decay rate-dependent criteria for the exponential stability of the considered neural networks are derived and presented in terms of linear matrix inequalities. Furthermore, the maximum allowable decay rate can be estimated based on the obtained results. Three numerical examples are given to demonstrate the effectiveness of the proposed method.

Robust asymptotic stability of fuzzy Markovian jumping genetic regulatory networks with time-varying delays by delay decomposition approach

In this paper, the robust asymptotic stability problem is considered for a class of fuzzy Markovian jumping genetic regulatory networks with uncertain parameters and switching probabilities by delay decomposition approach. The purpose of the addressed stability analysis problem is to establish an easy-to-verify condition under which the dynamics of the true concentrations of the messenger ribonucleic acid (mRNA) and protein is asymptotically stable irrespective of the norm-bounded modeling errors. A new Lyapunov–Krasovskii functional (LKF) is constructed by nonuniformly dividing the delay interval into multiple subinterval, and choosing proper functionals with different weighting matrices corresponding to different subintervals in the LKFs. Employing these new LKFs for the time-varying delays, a new delay-dependent stability criterion is established with Markovian jumping parameters by T–S fuzzy model. Note that the obtained results are formulated in terms of linear matrix inequality (LMI) that can efficiently solved by the LMI toolbox in Matlab. Numerical examples are exploited to illustrate the effectiveness of the proposed design procedures.

A delay-decomposition approach for stability of neural network with time-varying delay

This paper studies delay-dependent asymptotical stability problems for the neural system with time-varying delay. By dividing the whole interval into multiple segments such that each segment has a different Lyapunov matrix, some improved delay-dependent stability conditions are derived by employing an integral equality technique. A numerical example is given to demonstrate the effectiveness and less conservativeness of the proposed methods.

Stability analysis for neural networks with time-varying delay: A more general delay decomposition approach

This paper considers the stability analysis problem for neural networks with time-varying delay. Firstly, the new augmented Lyapunov functional is constructed by employing the more general decomposition approach. Then based on the Lyapunov stability theory and free weight matrix method, the novel delay-dependent stability condition is derived in terms of linear matrix inequalities (LMIs). Numerical examples show that the proposed method is more effective than some existing ones.