Dissipative filtering for semi-Markov jump singularly perturbed systems with a dynamic event-triggered mechanism

Abstract

The dissipative filter is designed in this paper via using a dynamic event-triggered approach for semi-Markov jump singularly perturbed systems. Based on the sampled-data, a novel dynamic event-triggered mechanism (ETM) is presented, where the threshold parameter dynamically adjusts according to continuously varying system output errors and modes. This approach adapts the threshold magnitude at the beginning to achieve better transient-time performance. The dynamic ETM offers more flexibility in data transmission, balancing system performance with transmission frequency. Furthermore, dissipative filter gains are designed by introducing non-singular matrices, eliminating the need for singular perturbation parameters. This method avoids ill-conditioning in the system and the singular perturbation parameter’s upper bound is estimated. Sufficient conditions for stochastically stable and desired dissipative performance of the filter error system are shown using the Lyapunov theory. Finally, the effectiveness of the proposed approach is validated through a numerical example and an RC circuit system.