Diagonal stability of uncertain interval systems

In this paper we consider the problem of diagonal stability of interval systems. We investigate the existence and evaluation of a common diagonal solution to the Lyapunov and Stein matrix inequalities for third order interval systems. We show that these problems are equivalent to minimax problem with polynomial goal functions. We suggest an interesting approach to solve the corresponding game problems. This approach uses the opennes property of the set of solutions. Examples show that the proposed method is effective and sufficiently fast.