Practical Stability Analysis of Systems with Delays and Periodic Coefficients

摘要

This paper deals with the numerical computation of the stability boundaries of delay differential equations with periodic coefficients in a two parameters space through autonomous approximations of the model. A first approximation is based on the averaging approach and analyzes the stability of an equilibrium of an autonomous system. The second approximation presented is based on the analysis of the stability of a particular periodic solution of an autonomous non-linear system. The stability of this solution is equivalent to the stability of an equilibrium of a periodic system which approximates the original system by using an arbitrary number of modes from the Fourier series of the periodic terms. These methods can be implemented with existing numerical tools, and two examples are presented: a simple periodic delay differential equation and a model of a milling process.