An H2 inner product, norm, output bounds, and first-order optimality conditions are derived for bilinear systems with quadratic outputs, and an iteration (BQO-TSIA) is shown to meet the conditions upon convergence.
Bilinear Quadratic Output Systems and Balanced Truncation
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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.
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math.NA 1years
2026 1verdicts
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Bilinear Systems with Quadratic Outputs: $\mathcal{H}_2$ Analysis, Optimality Conditions for Model Reduction, and Algorithmic Solutions
An H2 inner product, norm, output bounds, and first-order optimality conditions are derived for bilinear systems with quadratic outputs, and an iteration (BQO-TSIA) is shown to meet the conditions upon convergence.