Observer design for linear networked control systems using matrix inequalities

We design an observer-protocol pair to asymptotically reconstruct the states of a linear time-invariant (LTI) plant under network-induced communication constraints. We parameterize a class of observers and dynamic protocols, and for a given network transmission interval we derive sufficient conditions in terms of matrix inequalities for existence of an observer-protocol pair in the considered class that asymptotically reconstructs the plant states. The derived matrix inequalities are always feasible for sufficiently small transmission intervals if the underlying plant is observable from the measured output.