ON THE CALCULATION OF LYAPUNOV CHARACTERISTIC EXPONENTS FOR CONTINUOUS-TIME LTV DYNAMICAL SYSTEMS USING DYNAMIC EIGENVALUES

2012 ◽  
Vol 22 (01) ◽  
pp. 1250019
Author(s):  
MIGUEL ÁNGEL GUTIÉRREZ DE ANDA
Keyword(s):  
Dynamical Systems ◽  
Continuous Time ◽  
Linear Time ◽  
Analytic Solutions ◽  
Mean Value ◽  
Time Varying ◽  
Characteristic Exponents ◽  
Lyapunov Characteristic Exponents ◽  
The Mean ◽  
Time Linear

The concept of the dynamic eigenvalues may be used, in principle, to formulate in a general way analytic solutions of continuous-time linear time-varying dynamical (LTV) systems. It has also been suggested that the mean value of these quantities may be used to calculate Lyapunov characteristic exponents for the aforementioned systems. In this article, it will be demonstrated that this conjecture is not necessarily valid.

scholarly journals Models of Continuous-Time Linear Time-Varying Systems with Fully Adaptable System Modes

10.5772/5403 ◽  
2008 ◽  
Author(s):  
Miguel Angel Gutierrez de Anda ◽  
Arturo Sarmiento ◽  
Roman Kaszynski ◽  
Jacek Piskorowski
Keyword(s):  
Continuous Time ◽  
Linear Time ◽  
Time Varying ◽  
Time Varying Systems ◽  
Time Linear

SOME ANALYTIC CALCULATIONS OF THE CHARACTERISTIC EXPONENTS

2007 ◽  
Vol 17 (10) ◽  
pp. 3675-3678 ◽  
Author(s):  
P. VAN DER KLOET ◽  
F. L. NEERHOFF ◽  
N. H. WANING
Keyword(s):  
Dynamic Systems ◽  
Linear Time ◽  
Equilibrium Points ◽  
Analytic Solutions ◽  
Nonlinear Dynamic Systems ◽  
Time Varying ◽  
Variational Equations ◽  
Linear Time Invariant ◽  
Characteristic Exponents ◽  
Time Invariant

As is well known, the variational equations of nonlinear dynamic systems are linear time-varying (LTV) by nature. In the modal solutions for these LTV equations, the earlier introduced dynamic eigenvalues play a key role. They are closely related to the Lyapunov- and Floquet-exponents of the corresponding nonlinear systems. In this contribution, we present some simple examples for which analytic solutions exist. It is also demonstrated by example how the classical linear time-invariant (LTI) solutions are related to the equilibrium points of the general LTV solutions.

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