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.