Control sets of linear control systems on \R². The real case

2024/02/28 by Víctor Ayala, Ayala, Victor, Adriano Da Silva +3
Computer Science · #Mathematical Control Systems and Analysis

paper · pdf · doi:10.48550/arxiv.2402.18269

Abstract

In this paper, we study the dynamical behavior of a linear control system on \R² when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control range can have a strong interference in such dynamics if the matrix is not invertible. In the invertible case, we explicitly construct the unique control set with a nonempty interior.

Related

• Control sets of linear control systems on ℝ². The complex case
• The trouble with imaginary eigenvalues. Optimal control,\n controllability, frequency response
• Existence of eigensets on bilinear control systems
• Control sets of linear systems on semi-simple Lie groups
• Eigenstructure perturbations for a class of Hamiltonian matrices and solutions of related Riccati inequalities