2026/07/21 by Heike Faßbender, Serkan Gugercin, Till Peters
#math.NA #cs.NA #math.OC
Bilinear systems with quadratic outputs (BQO) have recently emerged as an important system class, arising naturally in applications where both the dynamics and the quantities of interest depend nonlinearly on the state. Despite the growing interest in this class of systems, a systematic H2 framework for BQO systems has been lacking. In this paper, we develop such a framework by establishing an H2 inner product and norm for BQO systems, deriving output bounds in terms of the H2 norm, and obtaining first-order optimality conditions for H2 optimal model reduction. Building on these theoretical foundations, we propose an algorithm that computes a reduced BQO system satisfying these optimality conditions, and thus generalizing existing H2 optimal methods for bilinear and linear quadratic output systems. The effectiveness of the proposed framework is demonstrated on two numerical examples.