This method, which provides a real ц upper bound, is based on linear algebraic manipulations and on the properties of the determinant (Jones, 1987). An upper bound of ц{М) is obtained as:

Подпись: (5.5). DMD-l<t> + (DMD~4)

mm max A(———————– 1——————- )

D Ф v 2

where A* denotes the complex conjugate transpose of A, A (A) is the largest eigenvalue of A, D is a real diagonal scaling matrix and Ф is a permutation matrix, defined as Ф = diag(± 1,±1,…). Since there are 2n matrices Ф to be considered in the case of an и dimensional vector S of parametric uncertainties, the method is here again exponential time.

This upper bound is proved in all cases to be less conservative than the upper bound of the complex s. s.v. of subsection 2.2. Note that the per­mutation matrix Ф may indicate a direction in the space of uncertainties which leads to instability.

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