On a linear time varying system and Liapunov criteria for stability
Ben Zion M. Naveh · AIAA Journal · 1976
and the eigenvalues of a positive-definite or sernidefinite matrix must be non-negative, Eq. (14) shows that the iteration procedure will be convergent for all errors { e ) if and only if the magnitudes of all eigenvalues of [KP]-[KS] are less than unity. To obtain some physical insight into this convergence criterion, assume that deflections corresponding to any eigenvector, {*,), are applied to the secondary structure at the interface points and that these are the only points that are loaded. Equation (3) shows that the load on the secondary structure is [Ks](Xi}.. Next, suppose that an equal and opposite load is applied to the primary structure. Equation (7) shows that the resulting deflection is [KP]-[Ks]lxi}=\\xl} (17)