This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.

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Summary This paper considers the stability and stabilization problems for the switched linear stochastic systems under dwell time constraints, where the considered systems can be composed of an arbitrary combination of stable and unstable subsystems. First, a time‐varying discretized Lyapunov function is constructed based on the projection of a linear Lagrange interpolant and a switching‐time‐dependent “weighted” function. The “weighted” function not only enforces the Lyapunov function to decrease at switching instants but also coordinates the dynamical behavior of the subsystems. As a result, some unified criteria for mean square stability and almost sure stability of the switched stochastic systems are established in terms of linear matrix inequalities. Based on the obtained stochastic stability criteria, 2 types of state feedback controllers for the systems are designed. Moreover, the novel results are applied to solve the intermittent control or the controller failure problems. Finally, conservatism analysis and numerical examples are provided to illustrate the effectiveness of the established theoretical results.

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