Exponential state estimate of positive systems with time-varying delays: a Lyapunov-Razumikhin approach

In this paper, for the first time, a linear Lyapunov-Razumikhin function is introduced to find an $\alpha$-exponential state estimate for positive systems with time delays. A new set of conditions for the existence of exponential state boundedness of positive systems with bounded time-varying delays is established. Two procedures are then proposed to find the factor vector of $\alpha$-exponential state estimate, in which some techniques of optimization are applied to find the smallest possible factor vector. Numerical experiments are presented to demonstrate the effectiveness of the linear Lyapunov-Razumikhin function as well as of the optimization techniques.