``Spike'' effect in Luenberger identifier for systems with multidimensional inputs and outputs (Q1175861)

This paper analyses the ``spike'' effect in linear state identifiers of linear systems. It is known that for scalar output systems, the construction of a Luenberger identifier with fast decaying initial errors results in large initial spikes. The situation its multivariable systems, becomes more complicated because the error matrix of the Luenberger identifier is not uniquely determined by its spectrum. In this paper, bounds on the ``spike'' in Luenberger identifiers of multivariable systems with a fairly general structure of the error matrix spectrum and arbitrary matrices realizing a given spectrum. The bounds are unimprovable in the order of the degree of stability.