Interconnection of Kronecker canonical form and special coordinate basis of multivariable linear systems

Abstract

This paper establishes a straightforward interconnection between the Kronecker canonical form and the special coordinate basis of linear systems. Such an interconnection yields an alternative approach for computing the Kronecker canonical form, and as a by-product, the Smith form, of the system matrix of general multivariable time-invariant linear systems. The overall procedure involves the transformation of a given system in the state-space description into the special coordinate basis, which is capable of explicitly displaying all the system structural properties, such as finite and infinite zero structures, as well as system invertibility structures. The computation of the Kronecker canonical form and Smith form of the system matrix is rather simple and straightforward once the given system is put under the special coordinate basis. The procedure is applicable to proper systems and singular systems.