SPECTRAL CHARACTERIZATION AND POLE ASSIGNMENT FOR POSITIVE LINEAR DISCRETE-TIME-SYSTEMS

The paper considers the spectral properties and the pole-assignment pr oblem for positive linear systems, recognizing that such systems are d efined on cones and not on linear spaces, so that the controls and sta te-space variables are restricted. Characterizations of spectra for si ngle-input single-output positive linear discrete-time systems with an d without the requirement on non-negativity of controls are derived in the form of systems of inequalities with a:special structure. Regions of admissible spectra for the second- and third-order positive linear systems are obtained, and their impact on the dynamical behaviour of the systems is analysed.