Nonlinear systems – algebraic gramians and model reduction

DOI10.1108/03321640510571147zbMath1082.93506OpenAlexW2146247463MaRDI QIDQ4672410

Marissa Condon, Rossen I. Ivanov

Publication date: 29 April 2005

Published in: COMPEL - The international journal for computation and mathematics in electrical and electronic engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1108/03321640510571147

Mathematics Subject Classification ID

Controllability (93B05) Nonlinear systems in control theory (93C10) Technical applications of optics and electromagnetic theory (78A55)

Related Items (7)

Interpolation-Based Model Order Reduction for Quadratic-Bilinear Systems and $${\mathcal {H}_{2}}$$ Optimal Approximation ⋮ Computational Methods for Linear Matrix Equations ⋮ $\mathcal H_2$-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems ⋮ Full state approximation by Galerkin projection reduced order models for stochastic and bilinear systems ⋮ Model reduction of controlled Fokker-Planck and Liouville-von Neumann equations ⋮ Krylov subspaces from bilinear representations of nonlinear systems ⋮ Bilinear Systems---A New Link to $\mathcal H_2$-norms, Relations to Stochastic Systems, and Further Properties

Cites Work

• Balancing for nonlinear systems
• Empirical balanced truncation of nonlinear systems
• Observability functions for linear and nonlinear systems.
• Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems
• Linear model reduction and solution of the algebraic Riccati equation by use of the sign function†
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• New model reduction scheme for bilinear systems
• Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals
• A subspace approach to balanced truncation for model reduction of nonlinear control systems
• Realization and Structure Theory of Bilinear Dynamical Systems
• On the nonuniqueness of singular value functions and balanced nonlinear realizations

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