ON CONTROLLABILITY AND OBSERVABILITY OF LINEAR SYSTEMS: MULTIPLE EIGENVALUE CASE

摘要

Thls paper presents a method to verify the controllability and observability of linear multivariable systems with multiple modes using eigenprojectors or constituent matrices. Eigenprojectors are obtained by the partial fraction expansion of the numerator of the transfer function matrix of the system and the constituent matrices are obtained from the spectral decomposition of the sate matrix. Eigenprojectors inform on the properties of the corresponding mode separately from the others, so controllability and observability of each mode are checked. A previous paper has dealt with linear systems with single eigenvalues, and the same method gave good results. Numerical examples are given to illustrate this method.