Robust Stability Analysis of Coupled Oscillators

Following Kharitonov's seminal theorem, a number of authors have developed criteria for analyzing the stability of a so-called polytope of polynomials. In this paper, we present a case study involving a polytope of polynomials carried out using the new results in [8]. More specifically, we consider a state space model describing a pair of coupled oscillators. Motivated by the fact that stability is guaranteed for small coupling, we consider the following question: How large can the off-diagonal interactions be before instabilty occurs? To this end, we use the new theory in [8] to generate bounds on the off-diagonal interactions under which stability is guaranteed. Our results indicate that these bounds increase as the frequency difference between the oscillators increases and as the damping increases.