Non-fragile $H_{\infty}$ state estimation for Markovian jumping singularly perturbed CVNs with missing measurements: An event-triggered strategy

Abstract

This article addresses the non-fragile $H_{\infty }$ state estimation problem for Markovian jumping singularly perturbed complex-valued networks (CVNs) with missing measurements. Firstly, a continuous-time stochastic CVN model is established, and a singular perturbation parameter is introduced to describe the common fast and slow dynamics of the presented system. Besides, to enhance communication efficiency and save network resources, a feasible event-triggered strategy is designed to handle missing data and ensure the robustness of the proposed state estimator. Furthermore, a novel Lyapunov-Krasovskii functional is constructed, which takes into account the singular perturbation parameter and Markovian switching modes. By resulting to Lyapunov stability theory and complex-valued matrix inequalities, several sufficient and convictive conditions are addressed to ensure derived that estimation error system can realize global asymptotic mean-square stability. In addition, the desired estimator gain matrices can be obtained by resolving a collection of matrix inequalities, and the robustness of the estimator against perturbations is also assessed. In the end of this paper, one numerical example with simulation is presented to verify effectiveness and reasonability of achieved theoretical results.