Robust \(H_{\infty}\) filtering for discrete-time Markov jump linear system with missing measurements (Q1666289)

Summary: The problem of robust \(H_{\infty}\) filtering is investigated for discrete-time Markov jump linear system (DMJLS) with uncertain parameters and missing measurements. The missing measurements process is modelled as a Bernoulli distributed sequence. A robust \(H_{\infty}\) filter is designed and sufficient conditions are established in terms of linear matrix inequalities via a mode-dependent Lyapunov function approach, such that, for all admissible uncertain parameters and missing measurements, the resulting filtering error system is robustly stochastically stable and a guaranteed \(H_{\infty}\) performance constraint is achieved. Furthermore, the optimal \(H_{\infty}\) performance index is subsequently obtained by solving a convex optimisation problem and the missing measurements effects on the \(H_{\infty}\) performance are evaluated. A numerical example is given to illustrate the feasibility and effectiveness of the proposed filter.