$H_{\infty}$ Filtering Design-Based Markov Jump Proprieties for Networked Control Systems

A novel and improved approach is provided for designing a filter in networked control systems (NCS) with Markovian jump processes, incorporating temporal delays and packet losses. In this approach, packet losses are modeled as a Bernoulli distribution, aiming to achieve the condition of stochastic stability for the filtering error system. The projection lemma is used to structure new analysis conditions and to involve some free-weighting matrices to reduce conservatism and guarantee a level of
$H_{\infty}$
performance. The proposed result is tested and confirmed by an example from the literature.