Work

Complexity of Output Feedback Stabilization

Year: 2026

Type: preprint

Abstract: We show that unless P = NP, there cannot be a polynomial-time (or even pseudo-polynomial-time) algorithm for output feedback stabilization of a linear dynamical system with a linear controller. This settles one of the best-known open problems in control theory. The result holds in both continuous and discrete time. We also present a family of stabilizable linear dynamical systems for which no polynomial-time algorithm can write down a stabilizing controller in its standard representation.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.20636

Authors: Ahmadi, Amir Ali, Chaudhry, Abraar, Narang, Ijay, Tang, Yukai

Institutions: University of Colorado Boulder, Georgia Institute of Technology, Princeton University

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213579085

Cites:

Cited by: 3

Related to: 10