American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Determining damping and potential coefficients of an inverse problem for a system of two coupled hyperbolic equations. Part I: Global uniqueness
  • PROC Home
  • This Issue
  • Next Article
    On optimal singular controls for a general SIR-model with vaccination and treatment
2011, 2011(Special): 991-1000. doi: 10.3934/proc.2011.2011.991

Spectral analysis for linear differential-algebraic equations

Vu Hoang Linh 1, and  Volker Mehrmann 2,

1. 

Faculty of Mathematics, Mechanics and Informatics, Vietnam National University, 334, Nguyen Trai Str., Thanh Xuan, Hanoi, Vietnam
2. 

Institut für Mathematik, MA 4-5, Technische Universität Berlin, D-10623 Berlin, Fed. Rep., Germany

Received  June 2010 Revised  February 2011 Published  October 2011

In this paper, the spectral theory of linear di fferential-algebraic equations (DAEs) is discussed. Lyapunov and Sacker-Sell spectra, which are well known for ordinary diff erential equations (ODEs), are studied for linear DAEs and their adjoint equations. The spectral properties of the DAEs are investigated via the so-called essentially underlying ODEs.
Keywords: di fferential-algebraic equation, Sacker-Sell spectrum, Lyapunov exponent, underlying ODE, exponential dichotomy..
Mathematics Subject Classification: Primary: 34D08, 34A09; Secondary: 34D09, 65L80.
Citation: Vu Hoang Linh, Volker Mehrmann. Spectral analysis for linear differential-algebraic equations. Conference Publications, 2011, 2011 (Special) : 991-1000. doi: 10.3934/proc.2011.2011.991
[1]

Jordi-Lluís Figueras, Thomas Ohlson Timoudas. Sharp $ \frac12 $-Hölder continuity of the Lyapunov exponent at the bottom of the spectrum for a class of Schrödinger cocycles. Discrete & Continuous Dynamical Systems, 2020, 40 (7) : 4519-4531. doi: 10.3934/dcds.2020189
[2]

Emmanuel Schenck. Exponential gaps in the length spectrum. Journal of Modern Dynamics, 2020, 16: 207-223. doi: 10.3934/jmd.2020007
[3]

Mihail Megan, Adina Luminiţa Sasu, Bogdan Sasu. Discrete admissibility and exponential dichotomy for evolution families. Discrete & Continuous Dynamical Systems, 2003, 9 (2) : 383-397. doi: 10.3934/dcds.2003.9.383
[4]

Thai Son Doan, Martin Rasmussen, Peter E. Kloeden. The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor. Discrete & Continuous Dynamical Systems - B, 2015, 20 (3) : 875-887. doi: 10.3934/dcdsb.2015.20.875
[5]

Bassam Fayad, A. Windsor. A dichotomy between discrete and continuous spectrum for a class of special flows over rotations. Journal of Modern Dynamics, 2007, 1 (1) : 107-122. doi: 10.3934/jmd.2007.1.107
[6]

Álvaro Castañeda, Gonzalo Robledo. Dichotomy spectrum and almost topological conjugacy on nonautonomus unbounded difference systems. Discrete & Continuous Dynamical Systems, 2018, 38 (5) : 2287-2304. doi: 10.3934/dcds.2018094
[7]

Abdallah Benabdallah, Mohsen Dlala. Rapid exponential stabilization by boundary state feedback for a class of coupled nonlinear ODE and $ 1-d $ heat diffusion equation. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021092
[8]

Jonathan DeWitt. Local Lyapunov spectrum rigidity of nilmanifold automorphisms. Journal of Modern Dynamics, 2021, 17: 65-109. doi: 10.3934/jmd.2021003
[9]

Keith Burns, Katrin Gelfert. Lyapunov spectrum for geodesic flows of rank 1 surfaces. Discrete & Continuous Dynamical Systems, 2014, 34 (5) : 1841-1872. doi: 10.3934/dcds.2014.34.1841
[10]

Alex Eskin, Maxim Kontsevich, Anton Zorich. Lyapunov spectrum of square-tiled cyclic covers. Journal of Modern Dynamics, 2011, 5 (2) : 319-353. doi: 10.3934/jmd.2011.5.319
[11]

Janusz Mierczyński, Wenxian Shen. Formulas for generalized principal Lyapunov exponent for parabolic PDEs. Discrete & Continuous Dynamical Systems - S, 2016, 9 (4) : 1189-1199. doi: 10.3934/dcdss.2016048
[12]

Pedro Duarte, Silvius Klein, Manuel Santos. A random cocycle with non Hölder Lyapunov exponent. Discrete & Continuous Dynamical Systems, 2019, 39 (8) : 4841-4861. doi: 10.3934/dcds.2019197
[13]

Sanjeeva Balasuriya. Uncertainty in finite-time Lyapunov exponent computations. Journal of Computational Dynamics, 2020, 7 (2) : 313-337. doi: 10.3934/jcd.2020013
[14]

Julien Grivaux, Pascal Hubert. Loci in strata of meromorphic quadratic differentials with fully degenerate Lyapunov spectrum. Journal of Modern Dynamics, 2014, 8 (1) : 61-73. doi: 10.3934/jmd.2014.8.61
[15]

Sigurdur Freyr Hafstein. A constructive converse Lyapunov theorem on exponential stability. Discrete & Continuous Dynamical Systems, 2004, 10 (3) : 657-678. doi: 10.3934/dcds.2004.10.657
[16]

Gabriel Fuhrmann, Jing Wang. Rectifiability of a class of invariant measures with one non-vanishing Lyapunov exponent. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 5747-5761. doi: 10.3934/dcds.2017249
[17]

Jinhao Liang. Positive Lyapunov exponent for a class of quasi-periodic cocycles. Discrete & Continuous Dynamical Systems, 2020, 40 (3) : 1361-1387. doi: 10.3934/dcds.2020080
[18]

Éder Rítis Aragão Costa. An extension of the concept of exponential dichotomy in Fréchet spaces which is stable under perturbation. Communications on Pure & Applied Analysis, 2019, 18 (2) : 845-868. doi: 10.3934/cpaa.2019041
[19]

Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020108
[20]

M. Sumon Hossain, M. Monir Uddin. Iterative methods for solving large sparse Lyapunov equations and application to model reduction of index 1 differential-algebraic-equations. Numerical Algebra, Control & Optimization, 2019, 9 (2) : 173-186. doi: 10.3934/naco.2019013

 Impact Factor: 

Tools

Metrics

  • PDF downloads (174)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences