Necessary and sufficient conditions for the stability of interval matrices

Establishes a set of new sufficient conditions for the Hurwitz and Schur stability of interval matrices. The authors use these results to establish necessary and sufficient conditions for the Hurwitz and Schur stability of interval matrices. The authors relate the above results to the existence of quadratic Lyapunov functions for linear time-invariant systems with interval-valued coefficient matrices. Using the above results, the authors develop an algorithm to determine the Hurwitz and the Schur stability properties of interval matrices. It is shown that the authors´ algorithm is applicable to very large classes of interval matrices and the authors prove that for such classes, the algorithm terminates in a finite number of steps. The authors demonstrate the applicability of their results by means of two specific examples.