Stability analysis of large‐scale dynamical systems by sub‐Gramian approach

DOI10.1002/rnc.3116zbMath1291.93234OpenAlexW1543090246MaRDI QIDQ5166427

I. B. Yadykin, Atlas V. Akhmetzyanov, Alexey Iskakov

Publication date: 26 June 2014

Published in: International Journal of Robust and Nonlinear Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/rnc.3116

zbMATH Keywords

Lyapunov equationmodel order reductionFaddeev matricesGramianlarge-scale dynamical systemssub-Gramian

Mathematics Subject Classification ID

Lyapunov and other classical stabilities (Lagrange, Poisson, (L^p, l^p), etc.) in control theory (93D05) System structure simplification (93B11) Control/observation systems governed by ordinary differential equations (93C15) Large-scale systems (93A15)

Related Items

Spectral decompositions for the solutions of Sylvester, Lyapunov, and Krein equations, Spectral and modal methods for studying stability and control of electric power systems, Detection of Energy Balance Anomalies in the Bilinear Dynamic Systems, Lyapunov modal analysis and participation factors applied to small-signal stability of power systems, A comparison of sub-Gramian analysis with eigenvalue analysis for stability estimation of large dynamical systems, Solution of the Lyapunov matrix differential equations by the frequency method, Energy approach to stability analysis of the linear stationary dynamic systems, Fault Tolerant Control of Power Grids, Integral solution of linear multi-term matrix equation and its spectral decompositions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On computational methods for Gramians of continuous dynamic systems
• On properties of gramians of continuous control systems
• Matrix sign function in the problems of analysis and design of the linear systems
• A modified low-rank Smith method for large-scale Lyapunov equations
• Numerical solution of the Lyapunov equation by approximate power iteration
• A Faddeev sequence method for solving Lyapunov and Sylvester equations
• Krylov Subspace Methods for Solving Large Lyapunov Equations
• THE EVALUATION OF INTEGRALS OF PRODUCTS OF LINEAR SYSTEM RESPONSES
• The principle of minimized iterations in the solution of the matrix eigenvalue problem