Non‐fragile state estimation of discrete‐time two‐time‐scale Markov jump complex networks subject to partially known probabilities.

Summary: This paper investigates the problem of non‐fragile H∞$$ {H}_{\infty } $$ state estimation for Markov jump complex networks with two‐time‐scale characteristics in discrete time, in which the transition probabilities information is partially known. A singular perturbation parameter reflects the two‐time‐scale property of Markov jump complex networks. The goal is to design a mode‐dependent state estimator to ensure that the estimation error system is stochastically stable and satisfies the H∞$$ {H}_{\infty } $$ performance index. By constructing a mode‐dependent Lyapunov function with the singular perturbation parameter, a sufficient condition based on the linear matrix inequality is obtained. By introducing an optimized relaxation matrix, a novel decoupling method is proposed for complex networks with two‐time‐scale characteristics to reduce the conservatism of the obtained state estimator. The usefulness of the intended state observer and the superiority of the unique decoupling approach provided are demonstrated numerically. [ABSTRACT FROM AUTHOR]