On Infinite-horizon Minimum Energy Control

TL;DR

This paper investigates the conditions under which the infinite-horizon minimum energy control problem has a solution for linear time-invariant systems, focusing on stabilizability and eigenvalue properties.

Contribution

It establishes necessary and sufficient conditions for the existence of solutions to the infinite-horizon minimum energy control problem for LTI systems.

Findings

Solution exists if and only if (A, B) is stabilizable and A has no imaginary eigenvalues.

Provides a complete characterization of solvability conditions for the problem.

Highlights the importance of eigenvalue placement in control design.

Abstract

We address the infinite-horizon minimum energy control problem for linear time-invariant finite-dimensional systems $(A, B)$. We show that the problem admits a solution if and only if $(A, B)$ is stabilizable and $A$ does not have imaginary eigenvalues.