ROBUST STABILITY OF INTERVAL MATRICES - A COMPUTATIONAL APPROACH

A simple computational procedure is given to determine the robust stab ility of matrices containing interval parameter uncertainty. The compu tation consists of determining the maximal phase difference of the cha racteristic polynomial, evaluated over the vertices of the uncertain p arameter set at each point of the stability boundary, and verifying th at this maximal phase difference is less than pi radians. This follows as a direct application of the 'mapping theorem', which allows us eff ectively to treat rank-one perturbations of matrices. We discuss the c onservatism of the method and show how the solution may be improved to any desired level of accuracy. We give several numerical examples of systems with state-space perturbations, and compare our results with t hose obtained by other methods.