Fast algorithms for exact and approximate feasibility of robust LMIs

We discuss fast randomized algorithms for determining an admissible solution for robust linear matrix inequalities (LMIs) of the form F(x, /spl Delta/)/spl les/0, where x is the optimization variable and /spl Delta/ is the uncertainty, which belongs to a given set /spl Delta/. The proposed algorithm is based on uncertainty randomization: it finds a solution in a finite number of iterations with probability one, if a strong feasibility condition holds. Otherwise, it computes a candidate solution which minimizes the expected value of a suitably selected feasibility indicator function. The theory is illustrated by examples of application to uncertain linear inequalities and quadratic stability of interval matrices.