Decentralised H∞-filtering of networked control systems: a jump system approach

We consider the problem of decentralised estimation of discrete-time interconnected systems with local estimators communicating with their subsystems over lossy communication channels. Assuming that the packet losses follow the Gilbert-Elliot model, the networked estimation problem can be formulated into a Markovian jump linear system framework. Modelling subsystem interactions as sum quadratic constrained uncertainties, we design mode-dependent decentralised H-infinity-estimators that robustly stabilise the estimator system and guarantee a given disturbance attenuation level. The estimation gains are derived with necessary and sufficient rank-constrained linear matrix inequality conditions. Results are also provided for local mode-dependent estimators. Estimator synthesis is done using a cone-complementarity linearisation algorithm for the rank-constraints. The results are illustrated via an example.