On Second Order Moment Lyapunov Spectrum for Markov Linear Impulse Dynamical Systems

15th Conference on Applied Mathematics (APLIMAT 2016): Proceedings 2016
Jevgeņijs Carkovs, Jolanta Goldšteine

The paper deals with the linear impulse dynamical system with the phase coordinates x(t) switched by homogeneous ergodic compound Poisson type Markov process y(t/ε) with moments of jumps εk, where ε is a small positive parameter. We construct the difference equation for the sequence Xk =x(εk) and prove that under some assumption there exists such a basis B(y,ε) in the space of symmetric matrices that the covariance matrices qk =E{ Xk Xk T} satisfies a linear iterative procedure qk = qk-1 Λ(ε). The developed method and algorithm we apply to finding of the second order moment Lyapunov spectrum for the initial impulse dynamical system.

Keywords
Impulse dynamical systems, Markov switching, moment reducibility, moment Lyapunov exponents.

Carkovs, J., Goldšteine, J. On Second Order Moment Lyapunov Spectrum for Markov Linear Impulse Dynamical Systems. In: 15th Conference on Applied Mathematics (APLIMAT 2016): Proceedings, Bratislava, 2-4 February, 2016. Bratislava: Slovak University of Thechnology, 2016, pp.177-188. ISBN 978-80-227-4531-4.

Publication language
English (en)