Delay-dependent Exponential Stability Criteria Research Articles

Delay‐dependent robust H ∞ filter design for uncertain neutral stochastic system with time‐varying delay

This study is concerned with the problem of the robust H ∞ filter design for uncertain neutral stochastic system with time-varying delay. With an appropriate augmented Lyapunov-Krasovskii functional formulated and a convex polyhedron method utilised, some novel delay-dependent exponential stability criteria for uncertain neutral stochastic system with time-varying delay are obtained in terms of linear matrix inequalities. Based on the obtained stability criteria, some sufficient conditions for the solvability of the robust H ∞ filter design are derived. The desired H ∞ filter is designed to guarantee the robustly exponential stability for the filtering error system with a prescribed H ∞ performance level. The novelty is that the desired results are obtained with less conservatism. Finally, two illustrative numerical examples are given to demonstrate the effectiveness of the authors obtained results.

Delay-dependent robust $$H_\infty $$ control for 2-D discrete nonlinear systems with state delays

This paper investigates the problem of robust $$H_\infty $$ control for a class of 2-D (two-dimensional) discrete state delayed systems with sector nonlinearity described by a model of Roesser type. Firstly, a delay-dependent sufficient condition of robust exponential stability for such 2-D discrete systems is derived in linear matrix inequalities (LMIs) form. Secondly, a delay-dependent exponential stability criterion with $$H_\infty $$ performance for the considered systems is also proposed. Then a state feedback $$H_\infty $$ controller is constructed based on the above results. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Improved delay-dependent exponential stability criteria for time-delay system

This paper considers the problem of time delay-dependent exponential stability criteria for the time-delay linear system. Utilizing the linear inequality matrices (LMIs) and slack matrices, a novel criterion based on the Lyapunov–Krasovskii methodology is derived for the exponential stability of the time-delay system. Based on the criteria condition we concluded that the upper bound of the exponential decay rate for the time-delay system can be easily calculated. In addition, an improved sufficient condition for the robust exponential stability of uncertain time-delay system is also proposed. Numerical examples are provided to show the effectiveness of our results. Comparisons between the results derived by our criteria and the one given in Liu (2004) [1], Mondie and Kharitonov (2005) [2], and Xu et al. (2006) [3] show that our methods are less conservative in general. Furthermore, numerical results also show that our criteria can guarantee larger exponential decay rates than the ones derived by Liu (2004) [1] and Mondie and Kharitonov (2005) [2] in all time delay points we have tested and in some of time delay points obtained by Xu et al. (2006) [3].

Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach

A novel approach is presented to realize the optimal exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov's direct method is proposed to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). According to the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level at the same time. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.

Novel Global Exponential Stability Criterion for Recurrent Neural Networks with Time-Varying Delay

The problem of global exponential stability for recurrent neural networks with time-varying delay is investigated. By dividing the time delay interval [0,τ(t)] intoK+1dynamical subintervals, a new Lyapunov-Krasovskii functional is introduced; then, a novel linear-matrix-inequality (LMI-) based delay-dependent exponential stability criterion is derived, which is less conservative than some previous literatures (Zhang et al., 2005; He et al., 2006; and Wu et al., 2008). An illustrate example is finally provided to show the effectiveness and the advantage of the proposed result.

Optimal Exponential Synchronization of Chaotic Systems with Multiple Time Delays via Fuzzy Control

This study presents an effective approach to realize the optimal <path id=x1D43B d=M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28 h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z /> <path id=x221E d=M983 225q0 -112 -67 -174.5t-150 -62.5q-91 0 -154.5 43.5t-113.5 129.5q-49 -85 -104 -129t-138 -44q-98 0 -158.5 66t-60.5 154q0 59 21 106.5t54.5 75.5t70.5 43t73 15q90 0 152.5 -43.5t112.5 -128.5q48 84 104.5 128t140.5 44q93 0 155 -65t62 -158zM478 196 q-27 49 -47 80t-50 67t-64 54t-73 18q-48 0 -81.5 -47t-33.5 -128q0 -96 37.5 -157.5t99.5 -61.5q68 0 117.5 47t94.5 128zM889 204q0 91 -35.5 151t-99.5 60q-68 0 -119 -47t-95 -127q27 -49 47 -80.5t50 -67.5t65 -54t74 -18q113 0 113 183z /> exponential synchronization of multiple time-delay chaotic (MTDC) systems. First, a neural network (NN) model is employed to approximate the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, this study proposes a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov’s direct method to ensure that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is provided to illustrate the concepts discussed throughout this work.

Delay distribution dependent stability criteria for interval time-varying delay systems

This paper studies the stability problem for linear systems with interval time-varying delay. By dividing the delay interval into two subintervals, delay-dependent exponential stability criterion and asymptotic stability criterion are obtained based on Lyapunov stability theory and reciprocally convex lemma. Furthermore, by assuming that the distribution of time delay is known, we allow that the derivative of Lyapunov–Krasovskii function have positive upper bound for the time delay in one subinterval, and get the delay distribution dependent stability criterion. We also extend the obtained criteria to the case that the delay interval is divided into more subintervals. The derived criteria are expressed in terms of Linear Matrix Inequalities (LMIs). Numerical examples are given to show the effectiveness of the proposed method.

Delay-dependent exponential stability for uncertain neutral stochastic linear systems with interval time-varying delay

This study mainly considers the problem for the robustly exponential stability of uncertain neutral stochastic linear systems with a delay varying in an interval. By constructing an augmented Lyapunov–Krasovskii functional, some new delay-dependent exponential stability criteria for such systems are established in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Three illustrative numerical examples are given to show the effectiveness of the proposed method.

Some improved criteria on exponential stability of neutral differential equation

In this paper, some improved delay-dependent exponential stability criteria of the neutral delayed differential equation are expressed in terms of linear matrix inequalities (LMIs). Compared with some existing ones, our results are derived without the use of the mode transformation method and the bounding technique. Three numerical examples are provided to show the effectiveness of the proposed method and less conservatism of the obtained results.

Novel Delay-Dependent Stability Criteria for Uncertain Discrete-Time Stochastic Neural Networks with Time-Varying Delays

This paper investigates the problem of exponential stability for a class of uncertain discrete-time stochastic neural network with time-varying delays. By constructing a suitable LyapunovKrasovskii functional, combining the stochastic stability theory, the free-weighting matrix method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Compared with some previous results, the new conditions obtain in this paper are less conservative. Finally, two numerical examples are exploited to show the usefulness of the results derived. Keywords—Delay-dependent stability; Neural networks; Timevarying delay; Linear matrix inequality(LMI).

New results for global exponential stability of neural networks with varying delays

In this paper, the problem of global exponential stability for a class of neural networks with interval time-varying delay is investigated. The time-delay pattern is quite general and including fast time-varyings. It is assumed that the time delay belongs to a given interval, but the derivative of a time-varying delay be less than 1 is removed, or the delay function is not necessary to be differentiable. By constructing a set of improved Lyapunov–Krasovskii functionals combined with a known integral inequality, new delay-dependent exponential stability criteria with explicitly exponential convergence rate are established in terms of LMIs (linear matrix inequalities). The stability criteria are less conservative than the existing results in the literatures. Numerical examples are given to illustrate the effectiveness of the results.

New Exponential Stability Criteria for Neural Networks With Time-Varying Delay

This brief is concerned with the global exponential stability analysis problem for neural networks with time-varying delay. We construct an augmented Lyapunov-Krasovskii functional by using the decompositions of the time delays. In order to deal with the integral terms, the different integral intervals with the same interval length are unified. As a result, no extra inequalities are involved. The novel delay-dependent exponential stability criterion is proposed. Numerical examples are given to demonstrate the effectiveness of the obtained results.

New delay-dependent exponential stability criteria for neural networks with discrete and distributed time-varying delays

In this paper, the problem of exponential stability criteria for neural networks with discrete and distributed time-varying delays are considered. By dividing the discrete delay interval into multiple segments and choosing a new class of Lyapunov functional which contains tripe-integral terms, some new delay-dependent stability criteria are derived in terms of linear matrix inequalities. The obtained criteria are less conservative because free-weighting matrices method and a convex optimization approach are considered. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Exponential $H_{\infty}$ Filter Design for Discrete Time-Delay Stochastic Systems With Markovian Jump Parameters and Missing Measurements

In this paper, the exponential H∞ filtering problem is studied for discrete time-delay stochastic systems with Markovian jump parameters and missing measurements. The measurement missing phenomenon, which is related to the modes of subsystems, is described in the form of random matrix function and the missing probability of each sensor at every mode is governed by an individual random variable taking values in the interval [0,1] . This description of missing measurements is more general than the existing ones, where the missing probability is described by a Bernoulli distribution white sequence or a certain diagonal matrix. By using Lyapunov method and the properties of conditional mathematical expectation, we propose a novel approach to achieve the delay-dependent exponential stability criterion such that the filtering error system is mean-square exponentially stable and satisfies a prescribed H∞ performance level. Moreover, there is no equation restriction on decay rate. Then, based on the obtained sufficient criterion, the filter matrices can be directly characterized by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to show the validity of the main result.

Global exponential stability of reaction—diffusion neural networks with discrete and distributed time-varying delays**Project partially supported by the National Natural Science Foundation of China (Grant No. 60974139) and partially supported by the Fundamental Research Funds for the Central Universities.

This paper investigates the global exponential stability of reaction—diffusion neural networks with discrete and distributed time-varying delays. By constructing a more general type of Lyapunov—Krasovskii functional combined with a free-weighting matrix approach and analysis techniques, delay-dependent exponential stability criteria are derived in the form of linear matrix inequalities. The obtained results are dependent on the size of the time-varying delays and the measure of the space, which are usually less conservative than delay-independent and space-independent ones. These results are easy to check, and improve upon the existing stability results. Some remarks are given to show the advantages of the obtained results over the previous results. A numerical example has been presented to show the usefulness of the derived linear matrix inequality (LMI)-based stability conditions.

Improved delay-dependent stability criteria for discrete-time stochastic neural networks with time-varying delays

This letter, investigates the problem of mean square exponential stability for a class of discrete-time stochastic neural network with time-varying delays. By constructing a appropriate Lyapunov-Krasovskii functional, combining the stochastic stability theory, and the convex theory method, a delay-dependent exponential stability criteria is obtained in term of LMIs. Finally, a numerical example is exploited to show the usefulness of the results derived.

A new delay-dependent exponential stability criterion for Itô stochastic systems with Markovian switching and time-varying delay

On the basis of the Lyapunov–Krasovskii method, the exponential stability in the mean square sense is investigated for Itô stochastic systems with Markovian switching and time-varying delay. The statistic properties of the Markov process and Brownian motion are employed to compute the constructed Lyapunov–Krasovskii functional of a rather general form. This enables us to make sense of the challenging problems in the stochastic framework, and then find a way to extend the techniques developed in the deterministic framework. Therefore, the stability conditions are established with the aid of some slack matrices and the boundary conditions on time-varying delay. Numerical examples are given to demonstrate the reduced conservatism.

Exponential Convergence Rate Estimation for a Class of BAM Neural Networks with Time-Delays

This paper is concerned with the exponential stability analysis problem for a class of neutral bidirectional associative memory (BAM) neural networks with parameter uncertainties and mixed time-delays where the parameter uncertainties are norm-bounded and the mixed time-delays involve discrete, distributed and neutral time-delays. By utilizing free-weighting matrix method and an appropriately constructed Lyapunov-Krasovskii Functional, some nove delay-dependent and decay-rate dependent exponential stability criteria are derived in the terms of linear matrix inequalities (LMIs). Meanwhile, the maximum allowable decay rate can be estimated based on the obtained results. Two numerical examples are presented to demonstrate the effectiveness of the proposed method.

Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays

This Letter investigates the problem of delay-dependent exponential stability analysis for uncertain stochastic neural networks with time-varying delay. Based on the Lyapunov stability theory, improved delay-dependent exponential stability criteria for the networks are established in terms of linear matrix inequalities (LMIs).

Delay-dependent exponential stability criteria for stochastic systems with polytopic-type uncertainties

This paper considers the problem of delay-dependent exponential stability in mean square for stochastic systems with polytopic-type uncertainties and time-varying delay. Applying the descriptor model transformation and introducing free weighting matrices, a new type of Lyapunov-Krasovskii functional is constructed based on linear matrix inequalities (LMIs), and some new delay-dependent criteria are obtained. These criteria include the delay-independent/ratedependent and delay-dependent/rate-independent exponential stability criteria. These new criteria are less conservative than existing ones. Numerical examples demonstrate that these new criteria are effective and are an improvement over existing ones.