TY - GEN
T1 - On the attainability of an estimate of a number of Perron exponents for discrete linear diagonal systems with bounded coefficients
AU - Konyukh, Alexander
AU - Niezabitowski, Michal
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/9/29
Y1 - 2015/9/29
N2 - The Lyapunov, Perron and Bohl exponents are the most important numerical characteristics of dynamic systems used in control theory. Properties of the first one are well investigated. Properties of the Perron and Bohl exponents are much less described in the literature, for example the questions about the structure of the sets of values of these quantities for general discrete-time systems are still open. In this paper we give an example of a two-dimensional system with bounded coefficients that have three different Perron exponents. In addition, we prove that the s-dimensional diagonal discrete-time system with bounded coefficients can have any number of different Perron exponents between 1 and 2s - 1.
AB - The Lyapunov, Perron and Bohl exponents are the most important numerical characteristics of dynamic systems used in control theory. Properties of the first one are well investigated. Properties of the Perron and Bohl exponents are much less described in the literature, for example the questions about the structure of the sets of values of these quantities for general discrete-time systems are still open. In this paper we give an example of a two-dimensional system with bounded coefficients that have three different Perron exponents. In addition, we prove that the s-dimensional diagonal discrete-time system with bounded coefficients can have any number of different Perron exponents between 1 and 2s - 1.
KW - Lyapunov exponent
KW - Perron exponent
KW - diagonal discrete time-varying systems
UR - https://www.scopus.com/pages/publications/84964499531
U2 - 10.1109/MMAR.2015.7284014
DO - 10.1109/MMAR.2015.7284014
M3 - Conference contribution
AN - SCOPUS:84964499531
T3 - 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015
SP - 994
EP - 999
BT - 2015 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 20th International Conference on Methods and Models in Automation and Robotics, MMAR 2015
Y2 - 24 August 2015 through 27 August 2015
ER -