On the number of upper Bohl exponents for diagonal discrete time-varying linear system

Abstract The Bohl exponents, similarly as the Lyapunov exponents, are one of the most important numerical characteristics of dynamical systems used in control theory. By contrast with properties of the Lyapunov characteristics, properties of the Bohl exponents are much less investigated. In this paper we present some new properties of the upper Bohl exponents of the diagonal discrete time-varying linear system.

[1]  Michał Niezabitowski.  On the Bohl and general exponents of the discrete time-varying linear system , 2014 .

[2]  K. Przyluski.  Remarks on the stability of linear infinite-dimensional discrete-time systems , 1988 .

[3]  Adam Czornik,et al.  On a continuity of characteristic exponents of linear discrete time-varying systems , 2012 .

[4]  M. V. Karpuk.  Lyapunov exponents of families of morphisms of metrized vector bundles as functions on the base of the bundle , 2014 .

[5]  Adam Czornik.  Bounds for characteristic exponents of discrete linear time varying systems , 2010, J. Frankl. Inst..

[6]  Aleksander Nawrat,et al.  Stability by the linear approximation for discrete equations , 2011 .

[7]  D. Hinrichsen,et al.  Mathematical Systems Theory I: Modelling, State Space Analysis, Stability and Robustness , 2010 .

[8]  A. Czornik,et al.  On the spectrum of discrete time-varying linear systems , 2013 .

[9]  A. Czornik,et al.  Corrigendum Lyapunov exponents for systems with unbounded coefficients , 2013 .

[10]  A. Czornik,et al.  On the perturbations preserving spectrum of discrete linear systems , 2011 .

[11]  A. Czornik,et al.  On the Lyapunov exponents of a class of second-order discrete time linear systems with bounded perturbations , 2013 .

[12]  S. N. Popova,et al.  Sufficient Conditions for the Local Proportional Controllability of Lyapunov Exponents of Linear Systems , 2003 .

[13]  Adam Czornik,et al.  Alternative formulae for lower general exponent of discrete linear time-varying systems , 2015, J. Frankl. Inst..

[14]  J. Klamka,et al.  On the Set of Perron Exponents of Discrete Linear Systems , 2014 .

[15]  A. Czornik,et al.  Lyapunov exponents for systems with unbounded coefficients , 2013 .

[16]  O. Perron.  Die Ordnungszahlen linearer Differentialgleichungssysteme , 1930 .

[17]  Aleksander Nawrat,et al.  On the stability of Lyapunov exponents of discrete linear systems , 2013, 2013 European Control Conference (ECC).

[18]  K. Maciej Przyłuski.  On asymptotic stability of linear time-varying infinite-dimensional systems , 1985 .

[19]  Aleksander Nawrat,et al.  Generalized spectral radius and Lyapunov exponents of linear time varying systems , 2007, 2007 IEEE International Conference on Control Applications.

[20]  Aleksander Nawrat,et al.  On new estimates for Lyapunov exponents of discrete time varying linear systems , 2010, Autom..

[21]  E. A. Barabanov,et al.  Necessary and sufficient conditions for the stability of Lyapunov exponents of linear differential systems with exponentially decaying perturbations , 2007 .

[22]  Adam Czornik,et al.  The relations between the senior upper general exponent and the upper Bohl exponents , 2014, 2014 19th International Conference on Methods and Models in Automation and Robotics (MMAR).

[23]  A. A. Kozlov,et al.  On the control of lyapunov exponents of linear systems in the nondegenerate case , 2007 .

[24]  A. M. Li︠a︡punov.  Stability of Motion , 2016 .

[25]  A. Czornik,et al.  On the Lyapunov and Bohl exponent of time-varying discrete linear system , 2012, 2012 20th Mediterranean Conference on Control & Automation (MED).

[26]  A. Czornik.  On the Perron exponents of discrete linear systems , 2010 .

[27]  A. Czornik,et al.  On the regularity of discrete linear systems , 2010 .

[28]  Michal Niezabitowski,et al.  About the properties of the upper Bohl exponents of diagonal discrete linear time-varying systems , 2014, 2014 19th International Conference on Methods and Models in Automation and Robotics (MMAR).

[29]  Stefan Rolewicz,et al.  On stability of linear time-varying infinite-dimensional discrete-time systems , 1984 .

[30]  Jerzy Klamka,et al.  About the number of the lower Bohl exponents of diagonal discrete linear time-varying systems , 2014, 11th IEEE International Conference on Control & Automation (ICCA).

[31]  Robert E. Vinograd.  SIMULTANEOUS ATTAINABILITY OF CENTRAL LYAPUNOV AND BOHL EXPONENTS FOR ODE LINEAR SYSTEMS , 1983 .

[32]  O. Perron,et al.  Die Stabilitätsfrage bei Differentialgleichungen , 1930 .

[33]  Aleksander Nawrat,et al.  Lyapunov Exponents for Discrete Time-Varying Systems , 2013 .

[34]  Adam Czornik,et al.  Set of possible values of maximal Lyapunov exponents of discrete time-varying linear system , 2008, Autom..

[35]  On the class of proper linear differential systems with unbounded coefficients , 2010 .

[36]  A. Czornik,et al.  On the perturbations of the Lyapunov exponents of discrete linear system , 2010 .