Bilinear quadratic output systems and balanced truncation
Abstract
Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various primal-dual formulations for these systems and define the corresponding system Gramians. Conditions for the existence and uniqueness of these Gramians are established, and the generalized Lyapunov equations they satisfy are derived. Using these Gramians and their truncated versions, which are computationally more efficient, we construct a balanced truncation framework for bilinear systems with quadratic outputs. The proposed approach is demonstrated through two numerical examples.
Fields of Study & Subjects
Advanced Control Systems Optimization
Publication details
- Journal / source
- International Journal of Control
- Publisher
- Informa UK Limited
- Volume
- 99
- Issue
- 10
- Pages
- 1–23
- Publication date
- 15 September 2026
- Language
- EN