Abstract
AbstractIn 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.
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