In the present paper a review is given of the important system theoretic concept of (A,B)-invariant subspace. The concept was introduced (with the name controlled invariant subspace) by Basile and Marro in 1969 [BM]. In 1970 this concept was rediscovered by Wonham and Morse [WM1]. The concept turned out to be of fundamental importance for numerous applications and for many theoretic investigations. It was the basis of the geometric approach to linear multivariable systems propagated by Wonham and Morse [WM,Wn]. Since there is another important development in linear system theory, the polynomial matrix approach (see e.g. [Ro], [Wo], [WD]) it is useful to obtain polynomial representations, or frequency domain characterizations of (A,B) -invariant subspaces in order to bridge the two diverging branches. Results of this type were obtained in [EB], [FW], [Ha4,5] and some of them will be mentioned here. In addition some properties and applications of stabilizability subspaces, introduced in [Ha5], are discussed. Also the relation between strong observability and strong detectability introduced in [PS], [Mo] (for discrete time) and (A,B)-invariant subspaces is indicated.
|ISSN van geprinte versie||0926-4493|