A geometric approach to the theory of 2-D systems

The authors develop a geometric approach to the theory of 2-D (two-dimensional) systems, defining in a suitable way the notion of (A/sub 1.2/, B/sub 1.2/)-invariant subspaces and of controlled invariant subspaces. Such subspaces are shown to have good computational and feedback properties, which make them useful in application. In particular, sufficient conditions and constructive procedures are obtained for the solutions of disturbance decoupling and model matching problems. Moreover, it is shown that certain structural properties of a 2-D system can be described by means of a set of indexes defined in geometric terms, and that such structural indexes can be used to reformulate the sufficient condition for model matching.<>