Laguerre domain identification of continuous linear time-delay systems from impulse response data

An expression for the Laguerre spectrum of the impulse response of a linear continuous time-invariant system with input or output delay is derived. A discrete state-space description of the time-delay system in the Laguerre shift operator is obtained opening up for the use of conventional identification techniques. A method for Laguerre domain identification of continuous time-delay systems from impulse response data is then proposed. Linear time-invariant systems resulting from cascading finite-dimensional dynamics with pure time delays are considered. Subspace identification is utilized for estimation of finite-dimensional dynamics. An application to blind identification of a mathematical model of an endocrine system with pulsatile regulation is also provided.