Mixed Mode-dependent Time Delays Research Articles

Mode-dependent stochastic synchronization criteria for Markovian hybrid neural networks with random coupling strengths

This paper is concerned with the stochastic synchronization problem for a class of Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time-delays in the mean square. First, a novel inequality is established which is a double integral form of the Wirtinger-based integral inequality. Next, by employing a novel augmented Lyapunov–Krasovskii functional (LKF) with several mode-dependent matrices, applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the auxiliary function-based integral inequalities, several novel delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent Markovian hybrid coupled neural networks. Finally, a numerical example with simulation is provided to illustrate the effectiveness of the presented criteria.

New stochastic synchronization criteria for fuzzy Markovian hybrid neural networks with random coupling strengths

This paper focuses on the stochastic synchronization problem for a class of fuzzy Markovian hybrid neural networks with random coupling strengths and mode-dependent mixed time delays in the mean square. First, a novel free-matrix-based single integral inequality and two novel free-matrix-based double integral inequalities are established. Next, by employing a novel augmented Lyapunov–Krasovskii functional with several mode-dependent matrices, applying the theory of Kronecker product of matrices, Barbalat’s Lemma and the new free-matrix-based integral inequalities, two delay-dependent conditions are established to achieve the globally stochastic synchronization for the mode-dependent fuzzy hybrid coupled neural networks. Finally, two numerical examples with simulation are provided to illustrate the effectiveness of the presented criteria.

Synchronization for complex dynamical networks with mixed mode-dependent time delays

In this paper, the problem of synchronization control is investigated for complex dynamical networks with discrete intervals and distributed time-varying delays. The main thing is to design a properly pinning controller, for which the error system of complex dynamical networks is asymptotically stable. Based on the theory of Lyapunov stability and linear matrix inequality, the suitable Lyapunov-Krasovskii functional is constructed in terms of the Kronecker product, and then we obtain a novel synchronization criterion. Finally, a numerical example is given to illustrate the effectiveness of the proposed methods.

Finite-time H∞ synchronization for complex dynamical networks with mixed mode-dependent time delays

This paper investigated the finite-time H∞ synchronization control for complex dynamical networks with mixed mode-dependent time delays. The complex dynamical networks system contains the general coupling term and the time-delay coupling term. The state feedback control is designed to ensure that the complex dynamical networks system is finite time H∞ synchronized. The sufficient conditions are established in the form of linear matrix inequalities by constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and using Kronecker product. In the last, a numerical example is given to demonstrate the effectiveness of proposed approach.

Passivity analysis of Markov jump BAM neural networks with mode-dependent mixed time-delays via piecewise-constant transition rates

Passivity problem is studied for Markov jump bi-directional associative memory (BAM) neural networks with both mode-dependent mixed time delays and time-varying transition rates. In this paper, we consider both discrete delay and distributed delay which are all switching based on Markov process r(t). Time-varying transition rates are, respectively, discussed under the cases of known transition rates and partly unknown transition rates. The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant. By utilizing LMIs technique and a class of Lyapunov functionals, a switching delay passivity criterion underlying known transition rates is derived, which can be easily checked by the Matlab LMI Tool Box. Furthermore, we extend the result to passivity analysis of Markov jump BAM neural networks with partly unknown transition rates. The results obtained relate on not only switching discrete delays but also switching distributed delays. Finally, a numerical example is given to illustrate the effectiveness of the results.

Exponential stability of Markovian jumping Cohen–Grossberg neural networks with mixed mode-dependent time-delays

In this paper, the exponential stability problem is investigated for a class of Cohen–Grossberg neural networks with Markovian jumping parameter and mixed time-delays. The mixed time-delays under consideration consist of both the mode-dependent discrete time-delays and the mode-dependent distributed time-delays. By constructing a new Lyapunov–Krasovskii functional and employing the stochastic analysis techniques, sufficient conditions are proposed to guarantee that the addressed neural networks are exponentially stable in the mean square sense. It is shown that the developed stability criteria can be easily verified by using the standard numerical software. Finally, an illustrative example is provided to show the feasibility and usefulness of the developed results.

Projective lag synchronization of Markovian jumping neural networks with mode-dependent mixed time-delays based on an integral sliding mode controller

In this paper, the mode-dependent projective synchronization problem of stochastic neural networks with mixed time-delays is investigated. By considering a proper sliding model surface, a sliding mode controller (SMC) is synthesized to guarantee the reach-ability of the specified sliding surface. The globally asymptotically stable of the sliding mode dynamical system is surveyed with the Lyapunov stability theory and linear matrix inequality (LMI) technique. A sufficient projective synchronization criterion for the stochastic neural networks is derived. Finally, numerical simulations are exploited to illustrate the effectiveness of the main results.

Synchronization of continuous-time Markovian jumping singular complex networks with mixed mode-dependent time delays

In this paper, the problem of globally synchronization is investigated for an array of N linearly coupled singular complex networks with Markovian jump and mixed time-delays. The complex network systems consist of m modes and the systems switch from one mode to another according to a Markovian chain with known transition probability. The time delays include discrete delays and distributed delays. The singular matrices in the consider systems are mode-dependent. By utilizing the Lyapunov–Krasovskii stability theory, linear matrix inequality (LMI) approach, stochastic analysis techniques and Kronecker product, some sufficient globally synchronization criteria are obtained. Several numerical examples are given to illustrate the feasibility and effectiveness of the proposed methods.

Non-fragile observer-based sliding mode control for Markovian jump systems with mixed mode-dependent time delays and input nonlinearity

This paper is concerned with the state estimation and the sliding mode control (SMC) for a class of Markovian jump systems with mixed mode-dependent time delays and input nonlinearity. A non-fragil...

Non-fragile observer-based sliding mode control for Markovian jump systems with mixed mode-dependent time delays and input nonlinearity

This paper is concerned with the state estimation and the sliding mode control (SMC) for a class of Markovian jump systems with mixed mode-dependent time delays and input nonlinearity. A non-fragile observer is designed to estimate the system states, and an observer-based SMC is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space. By constructing a novel mode-dependent Lyapunov–Krasovskii functional, some new criteria are established for the existence and the solvability of the desired observer-based sliding mode controller. Finally, numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results.

Optimal guaranteed cost control of a class of hybrid systems with mode-dependent mixed time delays

In this paper, the guaranteed cost control problem is investigated for a class of nonlinear systems with Markovian jumping parameters and mixed time delays. The time delays involved consist of the mode-dependent discrete time delay and the distributed time delay with mode-dependent upper and lower boundaries; the associated cost function is a quadratic function, and nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov–Krasovskii functionals and some analytic techniques, the sufficient conditions for the existence of guaranteed cost controllers are derived for the systems and related cost function. Moreover, a linear matrix inequality (LMI) based approach to design the optimal guaranteed cost controller is formulated to minimise the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.

On stabilization of stochastic Cohen-Grossberg neural networks with mode-dependent mixed time-delays and Markovian switching.

The globally exponential stabilization problem is investigated for a general class of stochastic Cohen-Grossberg neural networks with both Markovian jumping parameters and mixed mode-dependent time-delays. The mixed time-delays consist of both discrete and distributed delays. This paper aims to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. By introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive delay-dependent criteria for the exponential stabilization problem. Three numerical examples are carried out to demonstrate the feasibility of our delay-dependent stabilization criteria.

Robust stability of Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent delays

This article discusses the robust stability problem for a class of uncertain Markovian jump discrete-time neural networks with partly unknown transition probabilities and mixed mode-dependent time delays. The transition probabilities of the mode jumps are considered to be partly unknown, which relax the traditional assumption in Markovian jump systems that all of them must be completely known a priori. The mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jump modes. By employing the Lyapunov functional and linear matrix inequality approach, some sufficient criteria are derived for the robust stability of the underlying systems. A numerical example is exploited to illustrate the developed theory.

Dissipativity analysis of singular systems with Markovian jump parameters and mode-dependent mixed time-delays

In this paper, the problem of delay-dependent α-dissipativity analysis is investigated for a general class of singular systems with Markovian jump parameters and mode-dependent mixed time-delays. By using the novel Lyapunov–Krasovskii functional and stochastic analysis technology, the new criteria are derived to guarantee that the addressed singular systems are stochastically admissible and strictly (Q,R,S)-α-dissipative. Numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results.

Optimal Guaranteed Cost Control of a Class of Discrete-Time Nonlinear Systems with Markovian Switching and Mode-Dependent Mixed Time Delays

The guaranteed cost control problem is investigated for a class of nonlinear discrete-time systems with Markovian jumping parameters and mixed time delays. The mixed time delays involved consist of both the mode-dependent discrete delay and the distributed delay with mode-dependent lower bound. The associated cost function is of a quadratic summation form over the infinite horizon. The nonlinear functions are assumed to satisfy sector-bounded conditions. By introducing new Lyapunov-Krasovskii functionals and developing some new analysis techniques, sufficient conditions for the existence of guaranteed cost controllers are derived with respect to the given cost function. Moreover, a convex optimization approach is applied to search for the optimal guaranteed cost controller by minimizing the guaranteed cost of the closed-loop system. Numerical simulation is further carried out to demonstrate the effectiveness of the proposed methods.

Stabilizing and synchronizing the Markovian jumping neural networks with mode-dependent mixed delays based on quantized state feedback

In this paper, stabilization and synchronization control problems are considered for Markovian jumping neural networks with mode-dependent mixed time delays subject to quantization and packet dropout. By using the novel Lyapunov–Krasovskii functional, stochastic analysis technology and quantization feedback method, the stabilization problem is solved for the addressed neural networks firstly. Also, it is assumed that system state is quantized before being communicated. Then the sufficient condition for the existence of an admissible controller is established to ensure the asymptotic synchronization of the resulting closed-loop coupled neural networks. Finally, two numerical examples are presented to show the validity of our theoretical analysis results.

Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays

This paper is concerned with the stability problem for a class of Markovian jumping neutral-type neural networks with mode-dependent mixed time-delays. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. In addition, the distributed time-delays are characterized by the upper and lower bounds, both of which are mode-dependent. By constructing new Lyapunov–Krasovskii functionals, a unified framework is established to derive sufficient conditions for the concerned systems to be globally exponentially stable in mean square. A simulation example is provided to demonstrate the usefulness of the main results obtained.

Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays

In this technical note, the globally exponential stabilization problem is investigated for a general class of stochastic systems with both Markovian jumping parameters and mixed time-delays. The mixed mode-dependent time-delays consist of both discrete and distributed delays. We aim to design a memoryless state feedback controller such that the closed-loop system is stochastically exponentially stable in the mean square sense. First, by introducing a new Lyapunov-Krasovskii functional that accounts for the mode-dependent mixed delays, stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem. Then, a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality (LMI) approach. Finally, it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of LMIs. Numerical simulation is carried out to demonstrate the effectiveness of the proposed methods.

Stability and Synchronization of Discrete-Time Markovian Jumping Neural Networks With Mixed Mode-Dependent Time Delays

In this paper, we introduce a new class of discrete-time neural networks (DNNs) with Markovian jumping parameters as well as mode-dependent mixed time delays (both discrete and distributed time delays). Specifically, the parameters of the DNNs are subject to the switching from one to another at different times according to a Markov chain, and the mixed time delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. We first deal with the stability analysis problem of the addressed neural networks. A special inequality is developed to account for the mixed time delays in the discrete-time setting, and a novel Lyapunov-Krasovskii functional is put forward to reflect the mode-dependent time delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the stochastic stability. We then turn to the synchronization problem among an array of identical coupled Markovian jumping neural networks with mixed mode-dependent time delays. By utilizing the Lyapunov stability theory and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several LMIs are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to solve the stability analysis and synchronization problems of the class of neural networks under investigation, where the LMIs can be easily solved by using the available Matlab LMI toolbox. Two numerical examples are presented to illustrate the usefulness and effectiveness of the main results obtained.

State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays

In this Letter, we investigate the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters as well as mode-dependent mixed time-delays. The parameters of the discrete-time neural networks are subject to the switching from one mode to another at different times according to a Markov chain, and the mixed time-delays consist of both discrete and distributed delays that are dependent on the Markovian jumping mode. New techniques are developed to deal with the mixed time-delays in the discrete-time setting, and a novel Lyapunov–Krasovskii functional is put forward to reflect the mode-dependent time-delays. Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A numerical example is exploited to show the usefulness of the derived LMI-based conditions.