INVERSION OF MATRIX PENCILS FOR GENERALIZED SYSTEMS

This paper clarifies the nature of the Leverrier-Faddeev algorithm for generalized and state-space systems. It presents useful diagrams for recursive computation of the coefficients of the characteristic polynomial and the coefficient matrices of the adjoint matrix for various matrix pencils. A simplified case covers recursive equations and diagrams for inversion of the second-order matrix pencil (Es2+A1s+A0) where E may be singular. The appendix provides two examples of mechanical and heat exchange systems which can be described by the generalized models.