Nearest stable system using successive convex approximations

Stability is a crucial property in the study of dynamical systems. We focus on the problem of enforcing the stability of a system a posteriori  . The system can be a matrix or a polynomial either in continuous-time or in discrete-time. We present an algorithm that constructs a sequence of successive stable iterates that tend to a nearby stable approximation XX of a given system AA. The stable iterates are obtained by projecting AA onto the convex approximations of the set of stable systems. Some possible applications for this method are correcting the error arising from some noise in system identification and a possible solver for bilinear matrix inequalities based on convex approximations. In the case of polynomials, a fair complexity is achieved by finding a closed form solution to first order optimality conditions.