Stabilisation and control design by partial output feedback and by partial interconnection

Abstract

We study stabilisation and control design by partial output feedback on the one hand and by partial interconnection according to Willems on the other hand. This article is based on the paper Design, parametrization, and pole placement of stabilizing output feedback compensators via injective cogenerator quotient signal modules by I. Blumthaler and U. Oberst, and the same technique is used. Both discrete and continuous behaviours and various notions of stability are treated simultaneously. In the case of partial output feedback, we require that both the compensator and the feedback behaviour have proper transfer matrices without presuming properness of the plant. We obtain conditions ensuring the existence of such stabilising compensators which perform additional control tasks like, for instance, tracking, and an algorithm for constructing a large class of such compensators. In the case of stabilisation by interconnection no input–output structures of plant or compensator are assumed, but the controlled behaviour is endowed with a canonical input–output structure. Again we demand this input–output behaviour to have proper transfer matrix. For this situation we obtain necessary and sufficient conditions for the existence of compensators solving the given control task, and a constructive parametrisation of all of them

A Generalized Tracking and Disturbance Rejection Problem for Multidimensional Behaviors

“…In [2], the set-up introduced in [3] was generalized, to deal with more general stabilization goals (design of T-stabilizing compensators) and by introducing a target func-tion that can formalize a number of classical control problems, first of all the tracking of a reference signal, meanwhile rejecting a disturbance acting on the system.…”

“…The aim of this paper is to extend the results derived in [2] to the multidimensional case to deal with stabilization and regulation problems for nD behaviours. The main results derived in this manuscript represent neat, but highly non-trivial, generalizations of the results provided in section 4 of [2].…”

“…The aim of this paper is to extend the results derived in [2] to the multidimensional case to deal with stabilization and regulation problems for nD behaviours. The main results derived in this manuscript represent neat, but highly non-trivial, generalizations of the results provided in section 4 of [2]. Indeed, the mathematical set-up required to extend the analysis to the nD case deeply relies on advanced algebraic concepts, like Serre subcategories [16] and localization according to Gabriel [17].…”