Model matching problems for impulsive linear systems with polytopic uncertainties

Abstract

This work deals with the problem of designing a feedback compensator that forces the output of a linear system with abrupt discontinuities in the state evolution and polytopic uncertainties to match that of a given model with the same features. First, the case in which the system and the model are initialized at zero and output matching is required to be exact is considered. Then, the case in which, for arbitrary initialization, output matching is required to be asymptotic for sufficiently slow sequences of the time instants wherein the state exhibits abrupt discontinuities is studied. In addition, on the assumption that the model is stable for sufficiently slow jump time sequences, also the further requirement that asymptotic output matching be achieved with stability of the compensated system is investigated. Constructive, directly checkable, solvability conditions for the problems addressed are derived by leveraging on appropriate structural notions and geometric tools. Algorithmic procedures for the synthesis of the compensators, when the solvability conditions are met, are devised. Some illustrative examples conclude the work.