A structural approach to state-to-output decoupling

TL;DR

This paper presents a geometric control approach to solve a state-to-output decoupling problem, allowing for the distribution of system modes across outputs with conditions for solvability and a constructive method for controller design.

Contribution

It introduces necessary and sufficient conditions for state-to-output decoupling using geometric control and combinatorics, with a constructive solution method.

Findings

Conditions for solvability are expressed in terms of controlled invariant subspaces.

The approach is constructive, enabling explicit controller computation.

Solvability can be evaluated a priori from system data.

Abstract

In this paper, we address a general eigenstructure assignment problem where the objective is to distribute the closed-loop modes over the components of the system outputs in such a way that, if a certain mode appears in a given output, it is unobservable from any of the other output components. By linking classical geometric control results with the theory of combinatorics, we provide necessary and sufficient conditions for the solvability of this problem, herein referred to as state-to-output decoupling, under very mild assumptions. We propose solvability conditions expressed in terms of the dimensions of suitably defined controlled invariant subspaces of the system. In this way, the solvability of the problem can be evaluated a priori, in the sense that it is given in terms of the problem/system data. Finally, it is worth mentioning that the proposed approach is constructive, so that when a controller that solves the problem indeed exists, it can be readily computed by using the machinery developed in this paper.