Filter inputs with Markovian lossy links: Zero or hold?

This paper is concerned with ℋ₂ and ℋ_∞ filter design for discrete-time Markov jump systems. The Markov chain is used to model a lossy network and two different strategies used in practice are compared for the event of packet dropout. The zero-input strategy consists of providing the filter with null input in case of dropout, while the hold-input strategy consists of using the previous successfully transmitted value of the measurement as input in that case. We prove that both strategies are rigorously equivalent in terms of filtering performance. This result suggests that the zero-input strategy is always preferable than the hold-input strategy because its modeling is simpler and its implementation is cheaper than the latter. A numerical example illustrates the applicability of the results.