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This paper mainly studies the fixed-time synchronization of Markovian jump fuzzy cellular neural networks with stochastic perturbations, and time-varying delays in the leakage term. By designing delay-dependent controllers with or without fuzzy terms, constructing a suitable stochastic Lyapunov functional and using matrix analysis techniques, this paper derives some novel and useful sufficient conditions to guarantee the fixed-time synchronization of the addressed drive-response systems, and the conditions are delay-dependent, which has less conservative results. The finite time is also independent of the initial states. Finally, numerical examples are given to illustrate the effectiveness of the proposed main results.

This paper is concerned with mean square exponential synchronization for a class of Markovian switching complex networks (MSCNs) with time-varying delay and stochastic noise under feedback control and M-matrix approach. Firstly, a class of MSCNs with time-varying delay and stochastic noise is considered. Secondly, by using M-matrix method and feedback control scheme, several sufficient conditions of mean square exponential synchronization are derived. At last, two numerical examples and simulations are given to illustrate the effectiveness of the theoretical results.

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.

This paper concerns the stability analysis problem for stochastic delayed switched genetic regulatory networks (GRNs) with both stable and unstable subsystems. By employing the piecewise Lyapunov functional method combined with the average dwell time approach, we show that if the average dwell time is chosen sufficiently large and the derivative of the Lyapunov-like function for unstable subsystems is bounded by certain kind of continuous function, then exponential stability criteria of a desired degree are guaranteed. The derived results show that the minimal average dwell time is proportional to the time delays. Finally, an example is given to illustrate the effectiveness of the derived results.

In this paper, the problem of delay-dependent @a-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)-@a-dissipative. Numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results.

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.