Singular Value Decomposition of the First Markov Parameter

Abstract

As it has been observed in Chapter 4 the first nonzero Markov parameter of a linear discrete-time system (2.1) carries some amount of information concerning invariant and Smith zeros. The approach presented there has been based on the Moore-Penrose pseudoinverse of that parameter. It has been shown that in any nondegenerate system (2.1) with the first nonzero Markov parameter of full rank all system zeros are completely characterized as some eigenvalues of a real matrix of the order of the state matrix. Furthermore, it has been shown also that in such systems the invariant zeros may be found out as output decoupling zeros of an appropriate closed-loop (state feedback) system as well as that invariant and Smith zeros are one and the same thing.