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This paper deals with a unifying approach to the problems of computing theadmissible sets of parametrical multi perturbations in appropriate bounded setssuch that some fundamental properties of parameter-varying linear dynamicsystems are maintained provided that the so-called (i.e. perturbation-free)nominal system possesses such properties. The sets of parametrical multiperturbations include any combinations of parametrical multi perturbations inthe matrix of dynamics as well as in the control, output and input-outputinterconnection matrices which belong to some prescribed bounded domain in thecomplex space. The various properties which are investigated arecontrollability, observability, output controllability and existence of minimalstate-space realizations together with the associate existence or not ofassociate decoupling, transmission and invariant zeros. All the matrices ofparameters including the nominal and the disturbed ones which parameterize thedynamic system may be real or complex. The radii of the multi- parametricalperturbations are calculated in a simple way. The obtained results are thenapplied to systems subject to a finite number of point internal delays andparametrical multi perturbations by comparing the state- space descriptions ofsuch systems with the general descriptions previously investigated. Inparticular, the contributions of the delays to the spectral descriptions areassimilated to the contributions of a set of varying parameters in a domain forthe general description.

On the Fundamental Properties of Linear Parameter-Varying Dynamic  Systems Under Parametrical Multi-Perturbations. Applications to Time-Delay  Systems. Preliminary Results