Functional observers design for two interconnected linear systems via LMI

Abstract This paper proposes a functional observer for each subsystem of two interconnected system. An original expression of the observation error permits to use previous results on large scale delay systems to solve the problem. The proposed observers are free of interconnection terms and the observation error is unbiased. The observer are designed via some gains which are obtained via LMIs (i.e. via a tractable approach) from the Lyapunov-Krasovskii stability results. An algorithm is given for the computation of the observers, then a numerical example shows their effectiveness of this approach. This result can be extended for the H ∞ filtering of linear and nonlinear large scale systems.