Finite-time stabilization of memristive neural networks via two-phase method

The finite-time stability and stabilization issues of memristive neural networks with time delays are studied via two-phase method, based on impulsive control and state feedback control. Different from classical control design, the control scheme here consists of two phases, i. e. the state can reach the inner of the unit ball exponentially from any initial condition in the first phase, and the then it can arrive at zero equilibrium from the inner of the unit ball in a finite-time. By using different Lyapunov function in two phases, both the finite-time stability criteria based on algebra inequality and the settling time dependent on the initial condition are obtained simultaneously. Compare with the finite-time control strategy in the literature, the finite-time stability and finite-time controller for stabilization of memristive neural networks are used in the second phase only, rather than the whole control process. In addition, the pinning control based on our novel control scheme is designed to obtain the finite-time stabilization of memristive neural networks.