The existence and design of functional observers for two-dimensional systems

This paper is concerned with functional observers for two-dimensional (2D) systems described by the Fornasini–Marchesini local state-space second model. A necessary and sufficient condition is given for the existence of asymptotic functional observers. A more tractable necessary condition for the existence of asymptotic functional observers is also presented, as it helps exclude those 2D systems for which there is no asymptotic functional observer. A constructive design method is then proposed for the design of asymptotic functional observers using a rank condition on the given system matrices and a linear matrix inequality (LMI) technique. Two illustrative examples are provided to demonstrate the feasibility and effectiveness of the proposed method.