Delay Decomposition Research Articles

A delay decomposition approach to stability analysis of neutral systems with time-varying delay

This paper presents novel stability criteria for neutral systems with time-varying delay. By developing a delayed decomposition approach, 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). Then, based on the Lyapunov method, delay-dependent stability criteria are devised by taking the relationship between terms in the Leibniz-Newton formula into account. Criteria are derived in terms of LMIs, which can be easily solved by using various convex optimization algorithms. Three illustrative numerical examples are given to show less conservatism of our obtained results and the effectiveness of the proposed method.

Experiment Research of BDP/IFR Halogen Free Flame-Retarding for Oil-Extended SEBS

Bisphenol A bis (diphenyl) phosphate ester (BDP) and a kind of intumescent flame retardant (IFR) were used for flame retarding of oil-extended hydrogenated styrene-butylenes-styrene (O-SEBS). The samples were systemically characterized by TGA, LOI, UL-94, FTIR and FESEM; The results showed that, as a kind of plasticized flame retardant, BDP can improve thermal decomposition temperature and delay decomposition velocity of O-SEBS; while the IFR retardant can promote residual chars with multi-micro holes on the surface of SEBS to inhibit flame; Synergistic flame retarding effects were produced by using BDP and the IFR retardant together, with 20% BDP and 20% IFR, the LOI is 24.5 and flame retardant level is UL-94 classification of V-1, with no dripping. Meanwhile, SEBS-g-MA as compatibility can prompt char residual and thermal property of O-SEBS.

A delay decomposition approach to robust stability analysis of uncertain systems with time-varying delay

This paper is concerned with delay-dependent robust stability for uncertain systems with time-varying delays. The proposed method employs a suitable Lyapunov–Krasovskii's functional for new augmented system. Then, based on the Lyapunov method, a delay-dependent robust criterion is devised by taking the relationship between the terms in the Leibniz–Newton formula into account. By developing a delay decomposition approach, 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. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.

Robust [formula omitted] fuzzy control for uncertain nonlinear Markovian jump systems with time-varying delay

This paper investigates the problem of robust H∞ fuzzy control for a class of uncertain nonlinear Markovian jump systems with time-varying delay. The class of systems under consideration is described by the Takagi–Sugeno fuzzy model. The goal of the paper is to design a mode-dependent fuzzy state-feedback controller such that the closed-loop system is stochastically stable with a prescribed H∞ performance of disturbance attenuation for all admissible parameter uncertainties. In order to obtain a less conservative control design, a new stochastic Lyapunov–Krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals. Then, by employing this functional, a delay decomposition approach to the design of robust H∞ fuzzy controllers is developed in terms of linear matrix inequalities. Finally, two examples are given to illustrate the merit and usability of the proposed design method.

Further improvement of stability criterion and BRL for Markovian jump systems with interval time-varying delay

This paper deals with delay-dependent stochastic stability and bounded real lemma (BRL) for Markovian jump linear systems with interval time-varying delays. By constructing some new Lyapunov functionals and using the Jensen’s integral inequality method, the free weighting matrix method, the convex combination method and the delay decomposition approach integratedly, some less conservative delay-dependent stability criteria and BRL are established. Numerical examples are given to show the effectiveness of the proposed method.

Reliable Fuzzy Control for a Class of Nonlinear Networked Control Systems with Time Delay

AbstractThis paper is concerned with reliable fuzzy control for a class of nonlinear networked control systems (NCSs) with state delay and actuator failures. By utilizing the input delay approach, an equivalent continuous-time generalized Takagi-Sugeno (T-S) fuzzy model with both interval time-varying network-induced delay and data packet dropout is obtained. By employing the delay decomposition approach, the information of the states of delayed plant can be taken into full consideration. A sufficient condition is formulated in the form of a nonconvex matrix inequality, of which a feasible solution can be obtained by solving a minimization problem in terms of linear matrix inequality (LMI) with the cone complementarity linearization algorithm. The key features of the approach include the use of a tighter bounding technique (reciprocally convex combination lemma) and the introduction of uncorrelated augmented matrix items into the Lyapunov functional. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

Improved stability criteria for uncertain delayed neural networks

This paper is concerned with the stability problem of uncertain delayed neural networks. The system possesses time-varying and norm-bounded uncertainties. An improved integral inequality lemma is proposed to handle the cross-product terms occurred in the derivative of Lyapunov functional. By using the new lemma and a novel delay decomposition approach, new robust stability criteria for time varying delay neural networks with structured linear fractional form uncertainties are proposed in terms of LMIs. The sufficient conditions obtained in this paper are less conservative than those in the former literature.

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.

Novel delay-dependent stability criteria for neural networks with interval time-varying delay

The problem of delay-dependent asymptotic stability for neural networks with interval time-varying delay is investigated. Based on the idea of delay decomposition method, a new type of Lyapunov—Krasovskii functional is constructed. Several novel delay-dependent stability criteria are presented in terms of linear matrix inequality by using the Jensen integral inequality and a new convex combination technique. Numerical examples are given to demonstrate that the proposed method is effective and less conservative.

Some synchronization criteria for general complex networks with coupling delays

A general complex delayed dynamical network model with asymmetric coupling matrix is considered in this paper. For reducing the conservativeness of synchronization criteria, several novel synchronization stability conditions are presented by using delay decomposition methods. Numerical examples which are widely used to study delay-dependent synchronization stability are given to illustrate the effectiveness of the proposed methods.

Robust stability criteria for uncertain linear systems with interval time-varying delay

This paper considers the robust delay-dependent stability problem of a class of linear uncertain system with interval time-varying delay and proposes less conservative stability criteria for computing the maximum allowable bound of the delay range. Less conservatism of the proposed stability criteria is attributed to the delay-central point method of stability analysis, wherein the delay interval is partitioned into two subintervals of equal length, and the time derivative of a candidate Lyapunov-Krasovskii functional based on delay decomposition technique is evaluated in each of these delay segments. In deriving the stability conditions in LMI framework, neither model transformations nor bounding techniques using free-weighting matrix variables are employed for dealing the cross-terms that emerge from the time derivative of the Lyapunov-Krasovskii functional; instead, they are dealt using tighter integral inequalities. The proposed analysis subsequently yields a stability condition in convex LMI framework that can be solved using standard numerical packages. For deriving robust stability conditions, two categories of system uncertainties, namely, time-varying structured and polytopic-type uncertainties, are considered. The effectiveness of the proposed stability criteria is validated through standard numerical examples.

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

새로운 구간 분해 방법을 이용한 구간 시변지연을 갖는 선형시스템의 안정성

In this paper, we consider the stability of linear systems with an interval time-varying delay. It is known that the adoption of decomposition of delay improves the stability result. For the interval time-delay case, they applied it to the interval of time-delay and got less conservative results. Our basic idea is to apply the general decomposition to the low limit of delay as well as interval of time-delay. Based on this idea, by using the modified Lyapunov-Krasovskii functional and newly derived Lemma, we present a less conservative stability criterion expressed as in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

Note on stability of linear systems with time-varying delay

This note considers the stability of linear systems with a time-varying delay. We are interested in a simple Lyapunov–Krasovskii functional (LKF) approach without delay decomposition. In this category, all recent tractable results had a fixed bound on the allowable maximum size of the delay for years. We propose a new simple LKF including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function, and present a new result expressed in the form of LMIs. We show, by two well-known examples, that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time-delay.

Further result on reachable set bounding for linear uncertain polytopic systems with interval time-varying delays

The problem of reachable set estimation of linear uncertain polytopic time-varying delay systems subject to bounded peak inputs is studied in this paper. The delays considered in this paper are assumed to be non-differentiable and vary within an interval where the lower and upper bounds are known. Based on the Lyapunov–Krasovskii method and delay decomposition technique, a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one-dimensional search method and Matlab’s LMI Toolbox and allow us to find the smallest radius. A numerical example is given to illustrate the effectiveness of the proposed result.

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.

Stochastic Stability and Stabilization of Uncertain Jump Linear Delay Systems via Delay Decomposition

This paper studies the problem of robustly stochastic stability and stabilization for a class of uncertain Markov jump linear systems with time delay. A new stochastic Lyapunov–Krasovskii functional (LKF) is constructed for the stability analysis and stabilization, in which the delay is uniformly divided into multiple segments. Based on this LKF and using an improved Jensen's integral inequality, the improved delay-dependent stochastic stability criteria are first derived in terms of linear matrix inequalities (LMIs). Then, an LMI approach to the design of stabilizing controllers via delayed state feedback is developed. The previous stability criteria are extended to give the delay-dependent stabilization conditions in terms of LMIs. Furthermore, an LMI optimization algorithm is proposed to find the maximum allowable delay of the system. Finally, numerical examples show that the proposed results are effective and much less conservative than some existing results.