A new fixedtime stability theorem and its application to the fixedtime synchronization of neural networks Abstract   In this paper, we derive a new fixedtime stability theorem based on definite integral, variable substitution and some inequality techniques. The fixedtime stability criterion and the upper bound estimate formula for the settling time are different from those in the existing fixedtime stability theorems. Based on the new fixedtime stability theorem, the fixedtime synchronization of neural networks is investigated by designing feedback controller, and sufficient conditions are derived to guarantee the fixedtime synchronization of neural networks. To show the usability and superiority of the obtained theoretical results, we propose a secure communication scheme based on the fixedtime synchronization of neural networks. Numerical simulations illustrate that the new upper bound estimate formula for the settling time is much tighter than those in the existing fixedtime stability theorems. What is more, the plaintext signals can be recovered according to the new fixedtime stability theorem, while the plaintext signals can not be recovered according to the existing fixedtime stability theorems.

Prescribedtime decentralized regulation of uncertain nonlinear multiagent systems via output feedback Abstract   This paper addresses the global prescribedtime decentralized regulation problem for a family of uncertain nonlinear multiagent systems. The dynamics of each agent is supposed to be in the strict feedback form, where the uncertain nonlinearities admit Lipschitz growth conditions with an unknown positive constant gain multiplying by a timevarying continuous function gain. It is firstly defined error systems, which are composed of the leader and their followers, and shown that the prescribedtime decentralized regulation problem of the original systems is equivalent to the prescribedtime regulation problem of error systems. Then, by introducing a novel state transformation involving a timescaling function, the prescribedtime regulation problem is then converted into designing appropriate gain parameters. Finally, based on the Lyapunov stability theorem, the prescribedtime regulation of the closedloop systems is proved and the prescribedtime decentralized regulation of the original systems is thus guaranteed. An example is presented to show the feasibility of the proposed prescribedtime decentralized protocols.