Year: 2026
Type: preprint
Abstract: We study how actuator rank and control horizon jointly determine worst-case control performance for finite-dimensional linear systems under a fixed total actuator-gain budget. The design variable is the input covariance $X=BB^\top$. Scalar actuators give rank-one matrices $X=bb^\top$; dropping the rank constraint yields their convex hull and a semidefinite benchmark. We identify regimes in which low-rank designs necessarily fall short and others in which they attain the benchmark. At small time, the relaxed maximizer is unique and full rank. If $A$ is cyclic, then, for every $k
Source: arXiv (Cornell University)
Authors: Trélat, Emmanuel, Zuazua, Enrique
Institution: Laboratoire Jacques-Louis Lions
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Awards: G2972077997, G5350531418, G6033112984
OpenAlex ID: W7214949496