Interconnection of the Kronecker Canonical Form and Special Coordinate Basis of General Multivariable Linear Systems

This paper establishes a straightforward interconnection between the Kronecker canonical form andthe special coordinate basis of linear systems. Such an interconnection enables the computation ofthe Kronecker canonical form, and as a by-product, the Smith form, of the system matrix of generalmultivariable time-invariant linear systems. The overall procedure involves the transformation ofa given system in the state-space description into the special coordinate basis, which is capable ofexplicitly displaying all the system structural properties, such as finite and infinite zero structures, aswell as system invertibility structures. The computation of the Kronecker canonical form and Smithform of the system matrix is rather simple and straightforward once the given system is put under thespecial coordinate basis. The procedure is applicable to proper and singular systems.