An Observer for Time Lag Systems

An observer is presented for time lag systems described by state variable differential delay equations which dualizes a previously developed reducing transformation technique for state feedback stabilization. A system with delay in the state variables is shown to possess two characteristic matrix equations: a "left" matrix equation which arises in the feedback stabilization problem, and a "right" characteristic matrix equation which is shown to be central to the dualized observer problem. The resulting observer equation is similar in form to those developed in the literature using the spectral decomposition theory, but differs in constructive detail owing to the fact that its specification utilizes well known finite dimensional system techniques once the unstable pole set has been delineated.