On the Basic Assumptions in the Identification of Continuous Time Systems

Abstract

Linear dynamic continuous time systems are identified using discrete time or continuous time models. The identification using a discrete time model relies on the assumption that the excitation signal is piece wice constant (zero-order-hold), while the identification using a continuous time model relies on the assumption that the measured signals are band limited (they obey the Shannon sampling theorem). In practice discrete time models are often identified starting from band limited measurements and hence the question arises what kind of errors or problems these models introduce in for example the design of digital controllers. This paper studies the theoretical and practical implications of the use of discrete time and continuous time models in the identification of continuous time systems under the zero-order-hold as well as the band limited assumption.