All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds†

Keywords

Mathematics, Multivariable calculus, Singular value, Norm (philosophy), Approximations of π

References

• Matrices in control theory: with applications to linear programming,Stephen M. Barnett — 1971
• Dichotomies in Stability TheoryW. A. Coppel — 1978
• Optimization by Vector Space MethodsD. Luenberger — 1968
• ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEMVadim Adamjan, Damir Z. Arov, M. Г. Крейн — 1971
• Some theorems on the inertia of general matricesAlexander Ostrowski, Hans Schneider — 1962
• The approximation of one matrix by another of lower rankCarl Eckart, Gale Young — 1936
• Principal component analysis in linear systems: Controllability, observability, and model reductionB. Moore — 1981
• SYMMETRIC GAUGE FUNCTIONS AND UNITARILY INVARIANT NORMSL. Mirsky — 1960
• Inertia theorems for matrices, controllability, and linear vibrationsHȧrald K. Wimmer — 1974
• Model reduction via balanced state space representationsLars Pernebo, L. Silverman — 1982
• Banach Spaces of Analytic FunctionsGarrett Johnson, Kenneth A. Hoffman — 1962
• The Theory of MatricesFelix R. Gantmacher — 1984
• Introduction to matrix computationsG. W. Stewart — 1973
• On the factorization of rational matricesDante C. Youla — 1961
• On Bounded Bilinear FormsZeev Nehari — 1957
• Linear SystemsT. Kailath — 1980
• Real and complex analysisR. A. Rankin — 1968
• Introduction to Numerical AnalysisW. G., F. B. Hildebrand — 1976
• Optimal Hankel-norm model reductions: Multivariable systemsSun‐Yuan Kung, David W. Lin — 1980
• Optimal Hankel-norm approximation of continuous-time linear systemsDavid W. Lin, Sun Yuan Kung — 1982

Cited by

• H-infinity control : an exploratory studyAnette Boom — 1988
• Suboptimal Control for Higher Order Systems via Reduced Models Using Periodic Output FeedbackHerbert Werner, B. Bandyopadhyay — 1997
• Model order reduction for coupled systems using low-rank approximationsA Agnieszka Lutowska — 2012
• Model reduction techniques for large scale nuclear fusion devicesMassimo Fagherazzi — 2014
• Sufficient encoding of dynamical systemsFelix Creutzig — 2008
• PID Controller Design using BB-BCOA Optimized Reduced Order ModelS. R. Desai, Rajendra Prasad — 2012
• Dynamic-Data Driven Real-Time Identification for Electric Power SystemsShanshan Liu — 2009
• Stabilization of a class of stochastic nonlinear time-delay systemsZhinan Wang, James Lam, Xueqiang Liu — 2004
• A Degree Bound of the H∞-Optimal Solutions of the Robust Regulator ProblemQiong Wu, M. Mansour — 1990
• Consistent aeroelastic linearisation and reduced-order modelling in the dynamics of manoeuvring flexible aircraftHenrik Hesse — 2013
• Analytical Computation of Proper Orthogonal Decomposition Modes and n-Width Approximations for the Heat Equation with Boundary ControlTasha N. Fernandez — 2010
• Analysis and control of transitional shear flows using global modesShervin Bagheri — 2010
• Model reduction methods:in theory and applied on a hybrid-drive lineS.P. van den Bosch, van den — 1993
• Robust Control Design for Flight ControlWilliam H. Bennett, Harold G Kwatny, K. Glover — 1989
• Reduced-order modeling of power electronics components and systemsAli Davoudi — 2010
• Synthesis of 165-1165-1165-1-optimal linear feedback systemsM.S. Verma — 1988
• Well-conditioned computation for H∞ controller near the optimumVasile Drǎgan, Aristide Halanay, Adrian Stoica — 1997
• Computational Parabolic Inverse ProblemsGiulia Deolmi — 2012
• On Longitudinal Control of High Speed Aircraft in the Presence of Aeroelastic ModesSuresh M. Joshi, Atul Kelkar — 1996
• The Design of Low Order Controllers Using the Frobenius-Hankel NormRussell Allen Ramaker — 1990

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