Bilinear Systems---A New Link to $\mathcal H_2$-norms, Relations to Stochastic Systems, and Further Properties

DOI10.1137/19M1304106zbMath1467.93148arXiv1910.14427OpenAlexW3177758380MaRDI QIDQ5000633

Martin Redmann

Publication date: 15 July 2021

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.14427

zbMATH Keywords

reachabilityasymptotic stabilitybilinear systemsstochastic systemsmodel order reduction\(\mathcal{H}_2\)-error bounds

Mathematics Subject Classification ID

Nonlinear systems in control theory (93C10) Asymptotic stability in control theory (93D20) Stochastic systems in control theory (general) (93E03) Attainable sets, reachability (93B03)

Related Items (2)

Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems ⋮ Model order reduction for bilinear systems with non-zero initial states – different approaches with error bounds

Cites Work

• Unnamed Item
• Unnamed Item
• Positive operators and stable truncation
• Model reduction for stochastic systems
• A new type of singular perturbation approximation for stochastic bilinear systems
• Comments on integral variants of ISS
• Bilinear control processes. With applications to engineering, ecology, and medicine
• Asymptotic stability of the linear Ito equation in infinite dimensions
• Rational matrix equations in stochastic control.
• On \(H_2\) model reduction of bilinear systems
• Quasimonotonie und Ungleichungen in halbgeordneten Räumen
• An \(\mathcal{H}_2\)-type error bound for balancing-related model order reduction of linear systems with Lévy noise
• Infinite-dimensional bilinear and stochastic balanced truncation with explicit error bounds
• Balanced Averaging of Bilinear Systems with Applications to Stochastic Control
• Dual Pairs of Generalized Lyapunov Inequalities and Balanced Truncation of Stochastic Linear Systems
• Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems
• Type II Balanced Truncation for Deterministic Bilinear Control Systems
• $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems
• Type II Singular Perturbation Approximation for Linear Systems with Lévy Noise
• $\mathcal H_2$-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems
• Singular perturbation approximation for linear systems with Lévy noise
• Nonlinear systems – algebraic gramians and model reduction
• Interpolation-Based ${\cal H}_2$-Model Reduction of Bilinear Control Systems
• Energy estimates and model order reduction for stochastic bilinear systems
• Multipoint Volterra Series Interpolation and $\mathcal{H}_2$ Optimal Model Reduction of Bilinear Systems
• On a Matrix Riccati Equation of Stochastic Control
• Cross-Positive Matrices
• Approximation of Large-Scale Dynamical Systems

This page was built for publication: Bilinear Systems---A New Link to $\mathcal H_2$-norms, Relations to Stochastic Systems, and Further Properties