Realizations in Linear Systems Theory

Abstract

When a state variable description of a linear system is known, then its input–output behavior can be easily realized by interconnecting simpler components. The problem of realization refers to the following: given an input–output description such as the impulse response, or the transfer function in the case of time-invariant systems, find a state variable description, the impulse response of which is the given one. Existence and minimality conditions are discussed. We are interested in realizations of minimum order which is the case when the realization is both controllable and observable. Realizations in both the continuous-time and discrete-time systems are discussed.