Feedback equivalence and uniform ensemble reachability

TL;DR

This paper investigates feedback strategies to achieve uniform ensemble reachability in parameter-dependent linear systems, establishing conditions under which feedback can ensure this property when certain spectral and structural conditions are met.

Contribution

It demonstrates that feedback transformations can ensure uniform ensemble reachability if the system is pointwise reachable and its Kronecker indices are parameter-independent.

Findings

Feedback can ensure uniform ensemble reachability under certain spectral conditions.

Pointwise reachability is necessary for uniform ensemble reachability.

Kronecker indices independence from parameters is crucial for feedback design.

Abstract

This paper considers feedback methods for ensemble reachability of parameter-dependent linear systems $(A(\theta),B(\theta))$, where the parameter $\theta$ is varying over a compact Jordan arc in the complex plane. Recently, pointwise testable sufficient conditions for uniform ensemble reachability have been developed. Beside the necessity of pointwise reachablility these conditions put restrictions on the spectra of the matrices $A(\theta)$ and the Hermite indices of the pair $(A(\theta),B(\theta))$. In this paper we show that these conditions can be ensured by applying a suitable feedback transformation if the pair $(A(\theta),B(\theta))$ is pointwise reachable and it Kronecker indices are independent from the parameter.