On Two-Time Scale Decomposition of Positive Linear Systems

In this paper a natural two-time scale decomposition for the class of positive linear systems is addressed. Such class of systems are described by nonnegative state variables and positive or nonnegative matrices, and all variables involved are always at least nonnegative. Two situations related with the dynamics of systems described in two-time scales are analyzed: first, the case for positive linear systems and their corresponding two-time scale decomposition and then the case of positive systems having the so-called standard singularly perturbed form. In both cases some interesting properties are addressed. For a particular class of single-input single-output (SISO) positive linear systems the so-called inverse feedback control (positive control) is applied in order to track a positive step reference