ASYMPTOTIC MULTIVARIABLE ROOT-LOCUS BEHAVIOR FOR NON-PROPER SYSTEMS

The study of some of the fundamental geometric properties of the Markov parameters of linear, time-invariant and continuous systems has recently led to the extension of the classical root locus technique to the multivariable case. Most of the results derived however are restricted to the case of strictly proper systems. In the present paper an extension of the results concerning the asymptotic behavior of the root loci to systems with a direct pass from inputs to outputs is given; the results are derived as a natural generalization of already existing results when the Markov parameter chain is augmented in order to include the feed-forward operator of non-proper systems. A design procedure for the adjustment of the aymptotic behaviour is suggested and a simple numerical example is included in order to illustrate the effectiveness of the presented technique