Explanation of linear discrete time system behavior by singular value decomposition of the system matrix

Abstract

This study formulates the single-input-single-output (SISO) output controllability problem based on singular value decomposition (SVD) of the system matrix. With the approach, we show if any input trajectory is along a right singular vector, the output trajectory will be along the corresponding left singular vector and will mirror the input. In addition, we derive a relationship between zero locations and system matrix minimum singular values, σmin, and pole locations and system matrix maximum singular values, σmax, in the linear discrete time problem.