Finite‐time energy‐to‐peak filtering for Markov jump repeated scalar non‐linear systems with packet dropouts

This study is concerned with the finite‐time energy‐to‐peak filtering problem for Markov jump repeated scalar non‐linear systems with packet dropouts. The packet dropout phenomenon occurs in a random way and is modelled by a stochastic variable satisfying the Bernoulli distribution. The purpose of the study is to design a filter such that the resulting filtering error system is stochastically finite‐time bounded, and a prescribed energy‐to‐peak performance level is achieved over a finite time interval. By using the mode‐dependent diagonally dominant Lyapunov function approach, some strict linear matrix inequality‐based conditions are established for the existence of an admissible filter, and a corresponding explicit parameterisation of such a filter is obtained. Finally, a numerical example with simulation is presented to demonstrate the effectiveness of our proposed approach.