Hit-and-Run: new design technique for stabilization, robustness and optimization of linear systems

New randomized algorithms for stabilization and optimal control for linear systems are proposed. They are based on Hit-and-Run method, which allows generating random points in convex or nonconvex domains. These domains are either stability domain in the space of feedback controllers, or quadratic stability domain, or robust stability domain, or level set for a performance specification. By generating random points in the prescribed domain one can optimize some additional performance index. The approach demonstrated its high efficiency for numerous classical examples of design problems.