A Unified Theory of Model Reduction for Linear Time Invariant Dynamical Systems

Abstract

<p>The approximation of linear, time-invariant, dynamical systems by similar systems having fewer state variables is investigated. A class of reduced-order approximants called nonminimal partial realizations is introduced which includes many published methods as special cases, and thus represents a unification of the theory of model reduction. Since the concept of linear state variable feedback is central to many of the design procedures of modern control theory, the behaviour of the approximated system to such feedback laws derived from analysis of the approximating system is studied. The specific results derived give a credibility heretofore nonexistant to the class of reduced models called minimal partial realizations by virtue of the fact that they form a subclass of the nonminimal partial realizations. The use of canonical form state equations is advocated as a means of simplifying the computational procedure for an important class of reduced models termed aggregated partial realizations. Such realizations are shown to be useful for designing suboptimal linear quadratic servomechanism compensators, since guaranteed stability of the large-scale system is possible.</p>