Outlier-Resistant State Estimation for Singularly Perturbed Complex Networks With Nonhomogeneous Sojourn Probabilities

This study investigates an outlier-resistant state estimation problem for singularly perturbed complex networks (SPCNs) with sojourn probabilities and randomly occurring coupling strengths. Aiming at better describing the dynamic behavior of the network topology for SPCNs, a novel switching law associated with the time-varying sojourn probabilities is developed, and the variation of sojourn probabilities is arranged by a high-level deterministic switching signal. Meanwhile, a sequence of mode-dependent variables is employed to describe the randomly occurring coupling strength. Subsequently, to alleviate the side effects from possible measurement outliers, a dynamic saturation function-based state estimator is designed, whose saturation level is adaptively varying based on previous estimation errors. In virtue of Lyapunov theory and mode-dependent average dwell-time strategy, it can be verified that the resulting dynamics is stochastic
$\mathcal {H}_{\infty }$
finite-time bounded. To this end, a simulation example is presented to show the validity of the proposed estimator design method.