Markovian Jumping Complex Networks Research Articles

Asynchronous Synchronization of Markovian Jump Complex Networks With DoS Attacks and Distributed Communication Delays

Asynchronous Synchronization of Markovian Jump Complex Networks With DoS Attacks and Distributed Communication Delays

Quantized fault-tolerant pinning control for finite-time H∞ synchronization of T-S fuzzy discrete Markovian-jump complex networks subject to heterogeneous delays

This paper investigates the finite-time pinning synchronization problem for a class of T-S fuzzy discrete Markovian-jump complex networks (TSFDMCNs) influenced by heterogeneous delays. The evolution of system parameters follows the Markov jump process according to a transition probability matrix with partly unknown elements. Based on the system state output, quantized fault-tolerant pinning controller (QFTPC) is designed to overcome communication limitations and varying actuator fault. Besides, the asynchronous signal generated by the hidden Markov model is employed in controller to make full use of received information. A novel mode-dependent Lyapunov- Krasovskii functional (LKF) is established to guarantee the error system mean-square finite-time bounded with the prescribed performance. In order to reduce conservatism of derived results, an improved Wirtinger-based inequality technique is applied in considering both lower and upper bounds of different delay. Finally, simulation examples illustrate the effectiveness and meliority of the proposed theoretical methods.

Finite-Time Projective Lag Synchronization and Identification between Multiple Weights Markovian Jumping Complex Networks with Stochastic Perturbations

Two nonidentical dimension Markovian jumping complex networks with stochastic perturbations are taken as objects. The network models under two conditions including single weight and double weights are established, respectively, to study the problem of synchronization and identification. A finite-time projection lag synchronization method is proposed and the unknown parameters of the network are identified. First of all, based on Itô’s formula and the stability theory of finite-time, a credible finite-time adaptive controller is presented to guarantee the synchronization of two nonidentical dimension Markovian jumping complex networks with stochastic perturbations under both conditions. Meanwhile, in order to identify the uncertain parameters of the network with stochastic perturbations accurately, some corresponding sufficient conditions are given. Finally, numerical simulations under two working conditions are given to demonstrate the effectiveness and feasibility of the main theory result.

Finite-Time Synchronization of Markovian Jumping Complex Networks with Non-Identical Nodes and Impulsive Effects.

In this paper, we investigate the finite-time synchronization problem for a class of Markovian jumping complex networks (MJCNs) with non-identical nodes and impulsive effects. Sufficient conditions for the MJCNs are presented based on an M-matrix technique, Lyapunov function method, stochastic analysis technique, and suitable comparison systems to guarantee finite-time synchronization. At last, numerical examples are exploited to illustrate our theoretical results, and they testify the effectiveness of our results for complex dynamic systems.

Reduced-order filtering for networks with Markovian jumping parameters and missing measurements

ABSTRACTThe problem of reduced-order H∞ filters design for Markovian jumping complex networks with polytopic time-varying transition probability matrices is first addressed in this paper, where the dynamic of each node is described by the sector-bounded nonlinearity. For the measurements, both quantisation and packet dropouts are considered, where each node has its own packet dropout rate. By using the mode- and transition probability-dependent Lyapunov function approach, two sufficient conditions are provided to ensure the stochastic stability and the disturbance attenuation performance of the resulting filtering error system. Then, the mode-independent reduced-order filters design method is proposed, and the filter parameters are given explicitly by linear matrix inequality method. Finally, the effectiveness of the theoretic results presented is illustrated via a numerical example which contains performance comparison of different mode-independent reduced-order filters.

Finite-time synchronization of Markovian jump complex networks with generally uncertain transition rates

In this paper, finite-time synchronization for a class of Markovian jump complex networks (MJCNs) with generally uncertain transition rates (GUTRs) is considered. In this GUTR network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model is more general than partly unknown transition rates (PUTRs). By constructing a suitable stochastic Lyapunov–Krasovskii function, using finite-time stability theorem and pinning control approaches, a sufficient finite-time synchronization criterion is derived in term of linear matrix inequalities (LMIs), which is easy to solve with the help of the LMI toolbox in Matlab. Finally, theoretical results are supported by numerical simulations.

Exponential synchronization of delayed Markovian jump complex networks with generally uncertain transition rates

This paper investigates the exponential synchronization problem for a class of Markovian jump complex networks(MJCNs) with generally uncertain transition rates(GUTRs). In this GUTR neural network model, each transition rate can be completely unknown or only its estimate value is known. This new uncertain model could be applied to many practical cases. Based on the Lyapunov functional method and Kronecker product technique, a sufficient condition on the exponentially synchronization in mean square is derived in terms of linear matrix inequalities (LMIs)-which can be easily solved by using the Matlab LMI toolbox. Finally, one numerical example is well-studied to illustrate the effectiveness of the developed method.

Synchronization of Markovian jumping complex networks with event-triggered control**Project supported by the National Natural Science Foundation of China (Grant No. 11202084).

This paper investigates event-triggered synchronization for complex networks with Markovian jumping parameters. Nonlinear dynamics with Markovian jumping parameters is considered for each node in a complex network. By utilizing the proposed event-triggered strategy, and based on the Lyapunov functional method and linear matrix inequality technology, some sufficient conditions for synchronization of complex networks are derived whether the transition rate matrix for the Markov process is completely known or not. Finally, a numerical example is presented to illustrate the effectiveness of the proposed theoretical results.

Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov–Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.

Finite-time global synchronization for a class of Markovian jump complex networks with partially unknown transition rates under feedback control

This paper presents a framework for finite-time global synchronization of Markovian jump complex networks (MJCNs) with partially unknown transition rates, time-delays and stochastic noises. Several criteria for finite-time global synchronization are given by using the stochastic analysis techniques and matrix theory. These criteria provide a feasible approach to design linear feedback controller and to compute finite-time of global synchronization for the addressed MJCNs. Four numerical examples are given to demonstrate the effectiveness of the theoretical results.

Finite-time synchronization of Markovian jump complex networks with partially unknown transition rates

In this paper, finite-time synchronization problem is considered for a class of Markovian jump complex networks (MJCNs) with partially unknown transition rates. By constructing the suitable stochastic Lyapunov–Krasovskii functional, using finite-time stability theorem, inequality techniques and the pinning control technique, several sufficient criteria have been proposed to ensure the finite-time synchronization for the MJCNs with or without time delays. Since finite-time synchronization means the optimality in convergence time and has better robustness and disturbance rejection properties, this paper has important theory significance and practical application value. Finally, numerical simulations illustrated by mode jumping from one mode to another according to a Markovian chain with partially unknown transition probability verify the effectiveness of the proposed results.