  This paper deals with a unifying approach to the problems of computing the
admissible sets of parametrical multi perturbations in appropriate bounded sets
such that some fundamental properties of parameter-varying linear dynamic
systems are maintained provided that the so-called (i.e. perturbation-free)
nominal system possesses such properties. The sets of parametrical multi
perturbations include any combinations of parametrical multi perturbations in
the matrix of dynamics as well as in the control, output and input-output
interconnection matrices which belong to some prescribed bounded domain in the
complex space. The various properties which are investigated are
controllability, observability, output controllability and existence of minimal
state-space realizations together with the associate existence or not of
associate decoupling, transmission and invariant zeros. All the matrices of
parameters including the nominal and the disturbed ones which parameterize the
dynamic system may be real or complex. The radii of the multi- parametrical
perturbations are calculated in a simple way. The obtained results are then
applied to systems subject to a finite number of point internal delays and
parametrical multi perturbations by comparing the state- space descriptions of
such systems with the general descriptions previously investigated. In
particular, the contributions of the delays to the spectral descriptions are
assimilated to the contributions of a set of varying parameters in a domain for
the general description.
