Characteristic roots for Two-Lag Linear Delay Differential Equations
- D. M. Bortz
- Discrete and Continuous Dynamical Systems…
In this work, we establish characteristic roots of a linear scalar delay system with multiple discrete lags based on its Laplace transform. The computation of all eigenvalues relays on the Lambert W function. Our result shows that the number of eigenvalues located inside each branches (except for the principal branch) of the Lambert W function is the same as the total number of discrete delays. Once the characteristic roots in each branch of Lambert W functions are calculated, the time response of the delay system is then expressed as the sum of infinite series of exponentials acting on these roots. Numerical examples are presented to illustrate the results obtained.