New formulations of algebraic criteria for controllability and observability of a linear MIMO-system

Abstract

New formulations of algebraic criteria for controllability and observability of a linear dynamical system with multiple inputs and outputs (MIMO-systems) are given, the corresponding theorems are formulated. The criteria are based on algebraic relations between linear combinations of the control matrix columns and own vectors of the free dynamics matrix. Keywords algebraic criterion; controllability; observability; linear MIMO-system; own value; own vector; Krylov vector and matrix; kernel; cokernel