Characterization of the dissipative mappings and their application to perturbations of dissipative-Hamiltonian systems
Publication date :
15 June 2021
Journal title :
Numerical Linear Algebra with Applications
ISSN :
1070-5325
Publisher :
John Wiley & Sons, Hoboken, United States - New Jersey
Volume :
28
Issue :
6
Peer reviewed :
Peer Reviewed verified by ORBi
Research unit :
F151 - Mathématique et Recherche opérationnelle
Research institute :
R300 - Institut de Recherche en Technologies de l'Information et Sciences de l'Informatique R450 - Institut NUMEDIART pour les Technologies des Arts Numériques
Mackey DS, Mackey N, Tisseur F. Structured mapping problems for matrices associated with scalar products. Part I: Lie and Jordan algebras. SIAM J Matrix Anal Appl. 2008;29:1389–410.
Adhikari B. Backward perturbation and sensitivity analysis of structured polynomial eigenomial eigenvalue problem [PhD thesis]. I.I.T. Guwahati; 2008.
Adhikari B, Alam R. Structured Procrustes problem. Linear Algebra Appl. 2016;490:145–61.
Bora S, Karow M, Mehl C, Sharma P. Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures. SIAM J Matrix Anal Appl. 2014;35:453–75.
Bora S. Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures. SIAM J Matrix Anal Appl. 2015;36:393–416.
Mehl C, Mehrmann V, Sharma P. Stability radii for linear Hamiltonian systems with dissipation under structure-preserving perturbations. SIAM J Matrix Anal Appl. 2016;37:1625–54.
Mehl C, Mehrmann V, Sharma P. Stability radii for real linear Hamiltonian systems with perturbed dissipation. BIT Numer Math. 2017;57:811–43.
Overton ML, Van Dooren P. On computing the complex passivity radius. Paper presented at: Proceedings of the 44th IEEE Conference on Decision and Control. Melia Sevilla Hotel Seville, Spain: IEEE; 2005. p. 7960–4.
Golo G, Breedveld PC, Maschke BM, van der Schaft AJ. Hamiltonian formulation of bond graphs. In: Johansson ARR, editor. Nonlinear and hybrid systems in automotive control. Heidelberg, Germany: Springer-Verlag; 2003. p. 351–72.
van der Schaft AJ. Port-Hamiltonian systems: an introductory survey. In: Sanz-Sole JVM, Verdura J, editors. Proceedings of the International Congress of Mathematicians. Volume III. Madrid, Spain: European Mathematical Society Publishing House; 2006. p. 1339–65.
van der Schaft AJ, Maschke B. Port-Hamiltonian systems on graphs. SIAM J Control Optim. 2013;51:906–37.
Hinrichsen D, Pritchard AJ. Stability radii of linear systems. Syst Control Lett. 1986;7:1–10.
Hinrichsen D, Pritchard AJ. Composite systems with uncertain couplings of fixed structure: scaled Riccati equations and the problem of quadratic stability. SIAM J Control Optim. 2009;47:3037–75.
Jacob B, Möller S, Wyss C. Stability radius for infinite-dimensional interconnected systems. Syst Control Lett. 2020;138:104662.
Gillis N, Sharma P. On computing the distance to stability for matrices using linear dissipative Hamiltonian systems. Automatica. 2017;85:113–21.
Martins N, Lima L. Determination of suitable locations for power system stabilizers and static VAR compensators for damping electromechanical oscillations in large scale power systems. IEEE Trans Power Syst. 1990;5:1455–69.
Martins N, Pellanda P, Rommes J. Computation of transfer function dominant zeros with applications to oscillation damping control of large power systems. IEEE Trans Power Syst. 2007;22:1657–64.
Martins N. Efficient eigenvalue and frequency response methods applied to power system small-signal stability studies. IEEE Trans Power Syst. 1986;1:217–24.
Gräbner N, Mehrmann V, Quraishi S, Schröder C, von Wagner U. Numerical methods for parametric model reduction in the simulation of disc brake squeal. ZAMM-J Appl Math Mech / Zeitschrift für Angewandte Mathematik und Mechanik. 2016;96:1388–405.
Schiehlen W. Multibody systems handbook. Heidelberg, Germany: Springer-Verlag; 1990.
Horn R, Johnson C. Matrix analysis. Cambridge, MA: Cambridge University Press; 1985.
Albert A. Conditions for positive and nonnegative definiteness in terms of pseudoinverses. SIAM J Appl Math. 1969;17:434–40.
Alam R, Bora S, Karow M, Mehrmann V, Moro J. Perturbation theory for Hamiltonian matrices and the distance to bounded-realness. SIAM J Matrix Anal Appl. 2011;32:484–514.
Sun J. Backward perturbation analysis of certain characteristic subspaces. Numer Math. 1993;65:357–82.
Qiu L, Bernhardsson B, Rantzer A, Davison E, Young P, Doyle J. A formula for computation of the real stability radius. Automatica. 1995;31:879–90.
