Realizations in Linear Systems Theory

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 is the inverse of this process and can be formulated as follows: 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 or transfer function 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 reachable and observable. Realizations for both continuous-time and discrete-time systems are discussed