Functional observer and state feedback for input time–delay systems

The design of state functional observer and state feedback for systems with input time delays is addressed using the factorization approach in the frequency domain. The design needs to achieve the loop transfer recovery of direct state feedback by using the functional observer-based feedback control. A necessary and sufficient condition is given for the existence of the state functional observers for such systems. A parametrization for all observers of time-delay systems is proposed. Based on the results of the parametrization, the state functional observer and state feedback design procedure is presented. The computation can be implemented in state-space form using standard algorithms. Design examples are given to illustrate the procedure.