In previous works the authors proposed to use Hit-and-Run versions of Markov-chain Monte-Carlo algorithms for various problems of control and optimization. In this paper we focus on robust stabilization applications of the method. The crucial notion for this algorithm is a Boundary Oracle (BO), and we start with constructing BO for robustness problems, including robust stability of polynomials and robust LMIs. Numerical results for various control applications are presented. In particular, we consider a problem arising in control of helicopters. Simulations confirm that the randomized approach can be an effective tool for solving robust stability and robust stabilization problems.