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This paper studies the synchronization problem of coupled delayed multistable neural networks (NNs) with directed topology. To begin with, several sufficient conditions are developed in terms of algebraic inequalities such that every subnetwork has multiple locally exponentially stable periodic orbits or equilibrium points. Then two new concepts named dynamical multisynchronization (DMS) and static multisynchronization (SMS) are introduced to describe the two novel kinds of synchronization manifolds. Using the impulsive control strategy and the Razumikhin-type technique, some sufficient conditions for both the DMS and the SMS of the controlled coupled delayed multistable NNs with fixed and switching topologies are derived, respectively. Simulation examples are presented to illustrate the effectiveness of the proposed results.

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This paper concentrates the distributed formation containment problems for multiple unmanned aerial vehicle (UAV) systems under both fixed directed and switching directed topologies. The objective is to introduce the formation control into the containment control research, where master UAVs should exchange information with each other to achieve and maintain a desired formation. Then, two different control protocols are proposed for the master UAVs and slave UAVs, respectively. Utilizing the algebraic graph theory and stability theory, some sufficient conditions are derived to guarantee the master UAVs complete a prespecified formation, while the states of the slave UAVs converge to a convex hull formed by those of the master UAVs. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results.

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