Title :
On the Sigma Exponent of Discrete Linear Systems
Author :
Czornik, Adam ; Mokry, Piotr ; Nawrat, Aleksander
Author_Institution :
Dept. of Autom. Control, Silesian Tech. Univ., Gliwice, Poland
fDate :
6/1/2010 12:00:00 AM
Abstract :
In this technical note, we introduce the concepts of sigma exponent of discrete linear time varying system. It is shown that these exponents describe the possible changes in the Lyapunov exponents under perturbation decreasing at infinity at exponential rate. Finally we present formulas for the exponential exponents in terms of transition matrix of the system.
Keywords :
Lyapunov methods; asymptotic stability; discrete time systems; linear systems; perturbation techniques; time-varying systems; Lyapunov exponents; discrete linear time varying systems; perturbation technique; sigma exponent; transition matrix; Automatic control; Continuous time systems; Control system synthesis; Control systems; Difference equations; Frequency; H infinity control; Linear systems; Optimal control; Research and development; Rivers; Robust control; Robust stability; Robustness; Stability; Time invariant systems; Time varying systems; Uncertainty; Upper bound; Characteristic exponents; Lyapunov exponents; perturbation theory; time varying discrete linear systems;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2010.2045699
