J. Yogambigai

Synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude Kronecker product terms

The problem of synchronization is studied for complex dynamical networks with hybrid coupling delays on time scales. The hybrid coupling delays consist of both discrete and distributed coupling delays. Some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system. By employing the standard Lyapunov-Krasovskii functional, matrix expansion method to handle multitude Kronecker product terms and the modified Jensens inequalities on time scale, new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established interms of linear matrix inequality (LMI). Numerical examples are included to demonstrate the effectiveness of the proposed method.

Synchronization of master-slave markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control

Abstract In this article, a synchronization problem for master-slave Markovian switching complex dynamical networks with time-varying delays in nonlinear function via sliding mode control is investigated. On the basis of the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices, new synchronization criteria are derived in terms of linear matrix inequalities (LMIs). Then, an integral sliding surface is designed to guarantee synchronization of master-slave Markovian switching complex dynamical networks, and the suitable controller is synthesized to ensure that the trajectory of the closed-loop error system can be driven onto the prescribed sliding mode surface. By using Dynkins formula, we established the stochastic stablity of master-slave system. Finally, numerical example is provided to demonstrate the effectiveness of the obtained theoretical results.

Finite-time robust stochastic synchronization of uncertain Markovian complex dynamical networks with mixed time-varying delays and reaction–diffusion terms via impulsive control

Abstract This study examines the problem of finite-time robust stochastic synchronization of uncertain Markovian complex dynamical networks with mixed time-varying delays and reaction–diffusion terms via impulsive control. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. This paper proposes a complex dynamical network consisting of N linearly and diffusively coupled identical reaction–diffusion neural networks. By constructing a suitable Lyapunov–Krasovskii׳s (LK) functional and utilization of Jensen׳s inequality and Wirtinger׳s inequality, new synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

Passivity-based synchronization of stochastic switched complex dynamical networks with additive time-varying delays via impulsive control☆

Abstract The issue of passivity-based synchronization for switched complex dynamical networks with additive time-varying delays, stochastic and reaction–diffusion effects is investigated. In this paper, stochastic, passivity theory and impulsive control are taken to investigate this problem. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Ito differential rule and matrix analysis techniques, we established a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the switched complex dynamical networks is robustly passive in the sense of expectation. By constructing a suitable Lyapunov–Krasovskii functional using Jensen’s inequality, integral inequality technique and the passivity criterion of addressed complex dynamical networks is obtained. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares. Illustrative example is presented to demonstrate the effectiveness and usefulness of the proposed results.

Robust synchronization of uncertain Markovian jump complex dynamical networks with time-varying delays and reaction–diffusion terms via sampled-data control

Abstract This paper is concerned with the problem of robust synchronization of a class of complex dynamical networks with time-varying delays and reaction–diffusion terms. To reflect most of the dynamical behaviors of the system, the parameter uncertainties are considered. A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. The control objective is that the trajectories of the system by designing suitable control schemes track the trajectories of the system with sample-data control. It is shown that, through Lyapunov stability theory, the proposed sample-data controllers are successful in ensuring the achievement of robust synchronization of complex dynamical networks even in the case of uncertainity and Markovian jumping parameters. By utilizing the Lyapunov functional method, Jensen’s inequality, Wirtinger’s inequality and lower bounds theorem, we establish a sufficient criterion such that, for all admissible parameter uncertainties, the complex dynamical network is robustly synchronized. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Exponential Stability of Semi-Markovian Switching Complex Dynamical Networks with Mixed Time Varying Delays and Impulse Control

This study examines the problem of exponential stability of complex dynamical networks with impulse control and semi-Markovian switching parameters. By utilizing a supplementary variable technique and a plant transformation, the semi-Markovian switching complex dynamical networks can be equivalently expressed as its associated Markovian switching complex dynamical networks. By applying the Lyapunov stability theory, Jensen’s inequality, Dynkins formula, Schur complement and linear matrix inequality technique, some new delay-dependent conditions are derived to guarantee the exponential stability of the equilibrium point. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the results obtained.

Extended dissipative synchronization of complex dynamical networks with additive time-varying delay and discrete-time information

Abstract The problem of extended dissipativity analysis of complex dynamical networks with additive time-varying delays and discrete time information is considered in this article. By utilizing the Lyapunov functional method, Jensen’s inequality and free-weighting matrix analysis techniques, we established sufficient criterion such that the complex dynamical networks is synchronized. Further, the extended dissipativity analysis problem which contains H ∞ performance, passivity performance and L 2 − L ∞ performance in a unified framework is studied. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

Stochastic stability of neutral-type Markovian-jumping BAM neural networks with time varying delays

Abstract In this paper, stochastic stability of neutral type Markovian-jumping bidirectional associative memory (BAM) neural networks is investigated. The jumping parameters are modeled as a continuous-time discrete-state Markov chain. The activation functions are supposed to be bounded and globally Lipschitz continuous. Furthermore, based on the Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions and novel delay-dependent conditions are established for the stochastic asymptotic stability of Markovian jumping BAM neural networks. The condition is presented in terms of linear matrix inequalities (LMIs), which can be easily checked by using MATLAB LMI toolbox. Finally, numerical examples are provided to show the effectiveness of the main results.

Synchronization Criterion of Complex Dynamical Networks with Both Leakage Delay and Coupling Delay on Time Scales

The purpose of this paper is to investigate the problem of synchronization for complex dynamical networks with both leakage delay and coupling delay on time scales. Some novel and useful synchronization criteria of complex dynamical networks are derived based on stability theory of error dynamical system. By employing the standard Lyapunov–Krasovski functional and the modified Jensen’s inequalities on time scale, new sufficient conditions guaranteeing the global exponential stability of the origin of complex dynamical networks are established in terms of linear matrix inequality. Finally, numerical example is exploited to demonstrate the effectiveness of the proposed theoretical results.

Exponential Lagrange Stability for Markovian Jump Uncertain Neural Networks with Leakage Delay and Mixed Time-Varying Delays via Impulsive Control

The problem of exponential Lagrange stability analysis of Markovian jump neural networks with leakage delay and mixed time-varying delays is studied in this paper. By utilizing the Lyapunov functional method, employing free-weighting matrix approach and inequality techniques in matrix form, we establish several novel stability criteria such that, for all admissible parameter uncertainties, the suggested neural network is exponentially stable in Lagrange sense. The derived criteria are expressed in terms of linear matrix inequalities (LMIs). A numerical example is provided to manifest the validity of the proposed results.