Asynchronous Energy-to-Peak Filtering for Restricted Markov Jump Systems

This article focuses on settling the energy-to-peak filtering problem for Markov jump systems subject to multiple constraints. The transition probabilities (TPs) are assumed to be nonhomogeneous. Incessantly changed TPs are governed by upper-level transition probabilities (UTPs) belonging to a homogeneous Markov chain. First, a novel dual hidden Markov model is constructed to characterize the mismatched phenomena when asynchronizations occur to the system mode and the TP mode. Second, following the stochastic Lyapunov method, sufficient linear matrix inequality (LMI) conditions are presented to guarantee the existence of the asynchronous energy-to-peak full-order filter while simultaneously considering the nonlinear property of sensors. Third, the decoupling between the Lyapunov matrices and filter matrices is accomplished by a theoretically less conservative and computationally less arduous filtering technique. Then, the approach of designing asynchronous energy-to-peak filters extends to tackle different types of uncertain UTPs, thus adding more optional dimensions. Finally, the validity of established results is examined by two numerical examples.