The stability of linear time-varying discrete systems with time-delay (Q1342469)

The proposed stability criterion is based on a discretized version of the first Lyapunov method: determination of characteristic numbers of functions. The function \(\Omega\), constructed from the starting equation (1), is analogous to the Green function of a linear ODE. It permits in a well known fashion to reformulate equation (1) in a form analogue to the Cauchy integral representation, the delayed terms being the non- homogeneous part. The `integral' equation (2) is `solved' using a method similar to the approximation of solutions by Cauchy-Picard iterations. The growth rate of these `solutions' is estimated and a stability threshold is established. Like in the case of ODE's, such simple growth rate criteria do not cover critical and irregular Lyapunov cases.