English

The trouble with imaginary eigenvalues. Optimal control, controllability, frequency response

Optimization and Control 2022-02-01 v2

Abstract

We investigate a few problems in the theory of linear time-invariant systems that arise when the open-loop system possesses imaginary eigenvalues. The problems are: (1) the infinite horizon, minimum energy optimal control problem; (2) the matter of defining the controllability Gramian for systems that are not stable; (3) the regularity as a distribution of the Fourier transform of the state impulse response. Apart from separately investigating these problems, we also indicate how they are interconnected.

Keywords

Cite

@article{arxiv.2003.04374,
  title  = {The trouble with imaginary eigenvalues. Optimal control, controllability, frequency response},
  author = {Bahman Gharesifard and Andrew D. Lewis},
  journal= {arXiv preprint arXiv:2003.04374},
  year   = {2022}
}

Comments

There is an error in the manner in which the stabilising feedback is implemented in the case of multiple canonical blocks

R2 v1 2026-06-23T14:09:20.313Z