Control Laws and Adaptive Control of Linear Systems

Abstract

Let the set Y of output’s values be a linear space over the real number field R. It is well known that linear system theory was established in the algebraic sense [Kalman, 1969]. The main theorem says that for any causal linear input/output map, there exist at least two canonical (controllable and observable) linear systems which realize (faithfully describe) it and any two canonical linear systems with the same behavior are isomorphic.