Computation of Kronecker-like Forms of a System Pencil: Applications,Algorithms and Software.

Abstract

The reduction of system pencils to Kronecker-like canonical forms by orthogonal similiarity transformations has many important applilcations, as for example: in the poles-zeros analysis of a system; in the structural analysis of a system (controllability, stabilizability, observability, detectability); in computing inverse systems; in computing miniimum-phase factorizations of transfer-function matrices; in solving constrainted matrix Riccati equations; in computing the Kronecker's canonical form of a general pencil. The reduction of system pencils can be performed by specially tailored 0(n³) complexity numerically stable algorithms. The reduction technique can be also applied without modification to the more general case of an arbitrary pencil. A modular collection of LAPACK compatible FORTRAN 77 subroutines to perform the reduction of system pencil to several Kronecker-like forms is presented. Several lower level subroutines are useful in solving efficiently the above mentioned applications. A complete set of test programs together with a collection of test data accompanies the basic computational software.