Finite-time stability of state-dependent delayed systems and application to coupled neural networks

Abstract

Finite-time stability and stabilization problems of state-dependent delayed systems are studied in this paper. Different from discrete delays and time-dependent delays which can be well estimated over time, the information of state-dependent delays is usually hard to be estimated, especially when states are unknown or unmeasurable. To guarantee the stability of state-dependent delayed systems in the framework of finite time, a Razumikhin-type inequality is used, following which estimations on the settling time and the region of attraction are proposed. Moreover, the relationship between the variation speed of state-dependent delays and the size of the region of attraction is proposed. Then as an application of the theoretical result, finite-time stabilization is studied for a set of nonlinear coupled neural networks involving state-dependent transmission delay, where the design of memoryless finite-time controllers is addressed. Two numerical examples are given to show the effectiveness of the proposed results.

Keywords: Coupled neural networks; Finite-time stability; Lyapunov function; Razumikhin inequality; State-dependent delay.