On the Generation of Random Stable Polynomials

In this paper, we discuss various techniques for random generation of stable polynomials, both in discrete and continuous time. These different methods are presented in a unified framework – to provide a ``global vision" of the potentials of random generation techniques for stable polynomials. We first show how general-purpose random sampling schemes can be adapted to the problem at hand and present specific techniques for generation, discussing pro et contra of these methodologies. We then demonstrate how a whole class of random generation mechanisms can descend in an almost direct way from classical stability analysis tests. Also, Matlab implementation issues are duly considered. Possible applications to control are indicated and illustrative results of simulations are provided.