Time-varying polynomial matrix systems

Abstract

Differential polynomial matrices with coefficients meromorphic on an open interval I⊆R are studied first. The subclass of full matrices P (having the properties P is non-singular antl every local solution of Pf =0 extends analytically to I) forms a sublattice with respect to right division of square matrices which is anti-isomorphic to the lattice of the corresponding solution spaces. This and further properties are then exploited in the study of time-varying systems in differential operator representation. Results on equivalence, state space models, controllability/observability and transfer functions are derived.