Design of Rightmost Eigenvalues Using Distributed Delay

This paper considers the problem of designing the rightmost eigenvalues of linear scalar distributed delay systems using two different but complementary methods: generalized stability charts and matrix Lambert W functions. The generalized stability charts are based on generalized Hopf and fold curves that provide important insight into the problem, but the geometry of the curves may become complicated for certain delay distributions. The Lambert W function approach can be applied to general delay distributions, but requires numerical solutions which can suffer from convergence problems. We present simple examples for both approaches.