Delay-dependent Exponential Stability Criteria Research Articles

Exponential Stability of Delayed Generalized Neural Networks With Intermittent Large-Delay Periods

This article investigates the exponential stability of generalized neural networks (GNNs) with a time-varying delay. Different from the literatures on the similar topic, the considered time delay contains a few intermittent large-delay periods (LDPs). A new approach is proposed to determine how frequent and how long the LDPs are allowed for guaranteeing the exponential stability by using switching techniques. The GNN is first modeled as a switched time-delay system which may include an unstable subsystem. Then, based on a novel Lyapunov–Krasovskii functional with LDP-based terms, a delay-dependent exponential stability criterion and associated evaluation algorithm are developed. Finally, two numerical examples are provided to show the effectiveness of the proposed method.

Exponential H ∞ output tracking control for coupled switched systems with states of different dimensions

This paper is concerned with the output tracking control for complex switched systems with non-diffusively delayed coupling. The states' dimensions are different in the coupled switched systems and reference system. On the base of the average dwell time and piecewise Lyapunov functional methods, a delay-dependent exponential stability criterion is derived for the switched systems under the QUAD condition which is less conservative than the Lipschitz condition. The state feedback controller is employed in the design of output tracking, and the tracking performance is guaranteed by solving a linear matrix inequality. Finally, three numerical examples are provided to show the advantage and effectiveness of the proposed theoretical results.

Exponential stability criterion of the switched neural networks with time-varying delay

In this paper, the delay-dependent stability problem of the switched neural networks with time-varying delay is considered. By taking advantage of the average dwell time method and Lyapunov–Krasovskii functional (LKF) method, and using free-matrix-based integral inequality and the extended reciprocally convex matrix inequality, a less conservative delay-dependent exponential stability criterion in linear matrix inequalities (LMIs) is developed. Two numerical examples are given to demonstrate the benefits of the proposed criterion.

Extended dissipative estimator design for uncertain switched delayed neural networks via a novel triple integral inequality

This paper addresses the problem of extended dissipative estimator design for uncertain switched neural networks (SNNs) with mixed time-varying delays and general activation functions. Firstly, for dealing with triple integral term, a new integral inequality is derived. Secondly, based on the theory of convex combination, we propose a novel flexible delay division method and corresponding modified Lyapunov–Krasovskii functional (LKF) is established. Thirdly, a switching estimator design approach is contributed, which ensures that the resulting augmented system is extended dissipative. Combining the extended reciprocally convex technique with Wirtinger-based integral inequality, improved delay-dependent exponential stability criterion is obtained. Finally, a example with two cases is provided to illustrate the feasibility and effectiveness of the developed theoretical results.

Optimal fuzzy control of exponential synchronisation via genetic algorithm

ABSTRACTIn this study, a novel approach via GA-based fuzzy control is proposed to realize the exponential optimal H∞ synchronisation of MTDC systems. A robustness design of model-based fuzzy control is first presented to overcome the effect of modelling errors between the MTDC systems and T-S fuzzy models. Next, a delay-dependent exponential stability criterion is derived in terms of Lyapunov's direct method to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are reformulated into LMIs. According to the LMIs, a fuzzy controller is then synthesised to exponentially stabilise the error systems. Moreover, the capability of GA in random search for near-optimal solutions, the lower and upper bounds of the search space based on the feedback gains via LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers to speed up the synchronisation. Additionally, an IGA was proposed to overcome both the shortcomings of premature convergence of GA and local search. According to the IGA, a fuzzy controller is synthesised not only to realise the exponential synchronisation but also to achieve the optimal H∞ performance by minimising the disturbance attenuation level.

Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks.

This paper deals with the global exponential stability for delayed recurrent neural networks (DRNNs). By constructing an augmented Lyapunov-Krasovskii functional and adopting the reciprocally convex combination approach and Wirtinger-based integral inequality, delay-dependent global exponential stability criteria are derived in terms of linear matrix inequalities. Meanwhile, a general and effective method on global exponential stability analysis for DRNNs is given through a lemma, where the exponential convergence rate can be estimated. With this lemma, some global asymptotic stability criteria of DRNNs acquired in previous studies can be generalized to global exponential stability ones. Finally, a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results.

A neural-network-based exponential H∞ synchronisation for chaotic secure communication via improved genetic algorithm

ABSTRACTIn this study, a novel approach via improved genetic algorithm (IGA)-based fuzzy observer is proposed to realise exponential optimal H∞ synchronisation and secure communication in multiple time-delay chaotic (MTDC) systems. First, an original message is inserted into the MTDC system. Then, a neural-network (NN) model is employed to approximate the MTDC system. Next, 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 derived in terms of Lyapunov's direct method, thus ensuring that the trajectories of the slave system approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Due to GA's random global optimisation search capabilities, the lower and upper bounds of the search space can be set so that the GA will seek better fuzzy observer feedback gains, accelerating feedback gain-based synchronisation via the LMI-based approach. IGA, which exhibits better performance than traditional GA, is used to synthesise a fuzzy observer to not only realise the exponential synchronisation, but also achieve optimal H∞ performance by minimizing the disturbance attenuation level and recovering the transmitted message. Finally, a numerical example with simulations is given in order to demonstrate the effectiveness of our approach.

Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

This paper concerns managing the robust exponential stability problem of uncertain Takagi–Sugeno fuzzy systems with time-varying delay by employing a further improved integral inequality matrix approach. Based on the linear matrix inequality (LMI) approach, delay-dependent robust exponential stability criteria have been developed. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent robust exponential stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov–Krasovskii functionals. Maximum allowable upper bound for time-varying delays is determined. Numerical examples are provided to show that the obtained results significantly improve the allowed upper bounds of delay size over some methods existing in the literature.

Novel delay-dependent exponential stability criteria for neutral-type neural networks with non-differentiable time-varying discrete and neutral delays

In this paper, we consider exponential stability problem for neutral-type neural networks with both interval time-varying state and neutral-type delays under more generalized activation functions. We note that discrete and neutral delays are both time-varying where the discrete delay is not necessarily differentiable and the information on derivative of neutral delay is not required. To the best of our knowledge, this is the first study under this conditions on discrete and neutral delays. Furthermore, we consider the case when there are interconnections between past state derivatives, namely, neural networks contain activation function of past state derivatives. Based on the Lyapunov–Krasovskii functional, we derive new delay-dependent exponential stability criteria in terms of linear matrix inequalities (LMIs) which can be solved by various available algorithms. Finally, numerical examples are given to illustrate the effectiveness of theoretical results and to show less conservativeness than some existing results in the literature.

New Delay-Dependent Exponential Stability Criteria for Neural Networks with Mixed Time-Varying Delays

This study is concerned with the problem of new delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays via introducing a novel integral inequality approach. Specifically, first, by taking fully the relationship between the terms in the Leibniz-Newton formula into account, several improved delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). Second, together with some effective mathematical techniques and a convex optimization approach, less conservative conditions are derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF). Third, the proposed methods include the least numbers of decision variables while keeping the validity of the obtained results. Finally, three numerical examples with simulations are presented to illustrate the validity and advantages of the theoretical results.

Improved delay-dependent exponential stability criteria for neutral-delay systems with nonlinear uncertainties

In this paper, the problem of delay-dependent exponential stability criteria for neutral-delay system with nonlinear uncertainties is considered. By constructing a new class of Lyapunov–Krasovskii functionals and using the free-weighting matrices methods within a convex optimization approach, some less conservative delay-dependent stability criteria of neutral delay differential system with nonlinear uncertainties is obtained. These stability conditions are solved as linear matrix inequalities which can be easily solved by various convex optimization algorithms. Finally, numerical examples are given to illustrate the effectiveness of the results.

Delay‐dependent exponential stability for neutral stochastic system with multiple time‐varying delays

In this study, by constructing an appropriate Lyapunov–Krasovskii functional, one delay-dependent exponential stability criterion of neutral stochastic system with multiple time-varying delays is obtained in terms of linear matrix inequalities. The significant contributions of this study are that the fewer matrix variables in obtained results are involved and some less computational burdens are imposed. In particular, the obtained results can greatly reduce the conservatism when the multiple time-invariant delays case is considered. Finally, three illustrative numerical examples are given to show the effectiveness of our proposed results.

Robust Exponential Stability of Stochastic Discrete-Time BAM Neural Networks with Markovian Jumping Parameters and Delays

The problem of robustly globally exponential stability in the mean square is investigated for stochastic uncertain discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays and Markovian jumping parameters. The uncertainties are assumed to be the linear fractional form. By using Lyapunov-Krasovskii functional (LKF) method and some novel technique, a delay-dependent exponential stability criterion is established in terms of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness and the improvement of the proposed methods.

Delay-dependent robust [formula omitted] filter design for uncertain neutral stochastic systems with mixed delays

This paper is concerned with the problem of the robust L2–L∞ filter design for uncertain neutral stochastic systems with mixed delays. By constructing a modified Lyapunov–Krasovskii functional, some novel delay-dependent exponential stability criteria for uncertain neutral stochastic systems with mixed delays are established in terms of linear matrix inequality. And the obtained stability criteria pave the way for designing the robust L2–L∞ filter to guarantee the robustly exponential stability for the filtering error systems with a prescribed L2–L∞ performance level for all admissible uncertainties. Finally, three illustrative numerical examples are given to show the effectiveness of the obtained results.

Exponential synchronization of Markovian jumping neural networks with partly unknown transition probabilities via stochastic sampled-data control

This paper investigates the exponential synchronization for a class of delayed neural networks with Markovian jumping parameters and time varying delays. The considered transition probabilities are assumed to be partially unknown. In addition, the sampling period is assumed to be time-varying that switches between two different values in a random way with given probability. Several delay-dependent synchronization criteria have been derived to guarantee the exponential stability of the error systems and the master systems are stochastically synchronized with the slave systems. By introducing an improved Lyapunov–Krasovskii functional (LKF) including new triple integral terms, free-weighting matrices, partly unknown transition probabilities and combining both the convex combination technique and reciprocal convex technique, a delay-dependent exponential stability criteria is obtained in terms of linear matrix inequalities (LMIs). The information about the lower bound of the discrete time-varying delay is fully used in the LKF. Furthermore, the desired sampled-data synchronization controllers can be solved in terms of the solution to LMIs. Finally, numerical examples are provided to demonstrate the feasibility of the proposed estimation schemes from its gain matrices.

Delay-dependent exponential stability for uncertain neutral stochastic neural networks with interval time-varying delay

This paper is mainly concerned with the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic neural networks with interval time-varying delay. With an appropriate augmented Lyapunov–Krasovskii functional (LKF) formulated, the convex combination method is utilised to estimate the derivative of the LKF. Some new delay-dependent exponential stability criteria for such systems are obtained in terms of linear matrix inequalities, which involve fewer matrix variables and have less conservatism. Finally, two illustrative numerical examples are given to show the effectiveness of our obtained results.

Observer design of discrete-time impulsive switched nonlinear systems with time-varying delays

This paper investigates the problem of observer design for discrete-time impulsive switched nonlinear systems with time-varying delays. Firstly, based on the average dwell time approach and the Lyapunov–Krasovskii functional technique, a delay-dependent exponential stability criterion for the discrete-time impulsive switched nonlinear systems with time-varying delays is derived in terms of a set of linear matrix inequalities (LMIs). Then, sufficient conditions for the existence of an observer that guarantees the exponential stability of the corresponding error system are proposed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

New results on stability analysis for neutral stochastic linear system

In this study, the problem for the robustly exponential stability in mean square moment of uncertain neutral stochastic linear system with mixed time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii functional and utilising a convex polyhedron method, some new delay-dependent exponential stability criteria for such system are established in forms of linear matrix inequalities, which have less conservatism. Finally, three illustrative numerical examples are given to show the effectiveness of the obtained results.

Exponential [formula omitted] output tracking control for positive switched linear systems with time-varying delays

The problem of exponential L1 output tracking control for positive switched linear systems with time-varying delays is addressed in this paper. The exponential L1-gain performance index is introduced to study such a problem. By resorting to the average dwell time approach, and also by constructing an appropriate piecewise co-positive type Lyapunov–Krasovskii functional, a new delay-dependent exponential stability criterion is developed, and the exponential L1-gain performance is analyzed. Based on the results obtained, a state feedback controller is constructed such that the exponential L1 output tracking performance is satisfied. A numerical example is given to demonstrate the effectiveness of the proposed method.

Delay-dependent exponential stability criteria for neutral systems with interval time-varying delays and nonlinear perturbations

This paper investigates the problem of global exponential stability for neutral systems with interval time varying delays and nonlinear perturbations. It is assumed that the state delay belongs to a given interval, which means that both the lower and upper bounds of the time-varying delay are available. The uncertainties under consideration are norm-bounded. Based on the Lyapunov–Krasovskii stability theory, delay-partitioning technique and lower bounds lemma, less conservative delay-dependent exponential stability criteria are derived in terms of linear matrix inequalities (LMIs) with fewer decision variables than the existing ones. Numerical examples are given to show the effectiveness of the proposed method.