ON SECOND ORDER MOMENT LYAPUNOV SPECTRUM FOR MARKOV LINEAR IMPULSE DYNAMICAL SYSTEMS

摘要

The paper deals with the linear impulse dynamical system with the phase coordinate x(t) ∈Rd switched by a homogeneous ergodic compound Poisson type Markov process {y(t/∈),t ∈ R} with moments of jumps {∈Tk, k ∈ N}: where ∈ is a small positive parameter. We construct the difference equation for the sequence {Xk :=x(εrk)} and prove that under some assumption there exists such a basis {B(y,ε),y ∈ Y} in the space of symmetric d x d-matrices that the covariance matrices qk =E{XkX~T_kB(y(rk),e)} satisfy a linear iterative procedure qk= qk-1A{∈). We apply the developed method and algorithm to finding of the second order moment Lyapunov spectrum for the initial impulse dynamical system.