Existence and Design of Target Output Controllers
Tyrone Fernando, Mohamed Darouach
TL;DR
This work develops a rigorous framework for target output controllability, focusing on steering $z(t)=F x(t)$ rather than all states. It introduces a PBH-type and rank-based criterion that corrects previous results, and provides existence conditions for designing target output controllers by placing either $r$ or $n_0$ poles, using generalized inverses and pole-placement of reduced subsystems. A practical design algorithm is proposed, including a static output feedback variant when $F=C$, and augmented-output strategies with $FR$ to relax conditions. Numerical examples on uncontrollable/unobservable systems validate the theory and illustrate controller design in both full-state and target-output contexts. Collectively, the results extend full state feedback principles to target outputs and offer actionable methods for controller synthesis under partial controllability.
Abstract
This paper introduces new conditions for target output controllability and provides existence conditions for placing a specific number of poles with a target output controller. Additionally, an algorithm is presented for the design of a target output controller. Controllability of the system under consideration is not required for designing target output controllers in this context. The findings in this paper extend the principles of full state feedback control. Moreover, we present conditions for static output feedback control under specific constraints. Several numerical examples are provided to illustrate the results.