Research ArticleOpen AccessGoogle Scholar indexed
Analyzing the Stability of a <i>n-DOF</i> System with Viscous Damping
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
- 1 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
- 2
Copy link · social · email
Abstract
In this paper we introduce a numerically stable method for determining the stability of n-DOF system without computing eigenvalues. In this sense, at first we reduce the second-order system to a standard eigenvalue problem with symmetric tridiagonal form. Then we compute the exact inertia by using an algorithm based on floating point arithmetic [1]. Numerical tests report the effectiveness of these methods.
Keywords<i>n-DOF</i>SystemInertiaStabilityLanczos
- K. V. Fernando, “Computation of Exact Inertia and Inclusions of Eigenvalues of Tridiagonal Matrices,” Linear Algebra and Its Applications, Vol. 422, No. 1, 2007, pp. 71-99. doi:10.1016/j.laa.2006.09.008
- D. Carlson and B. N. Datta, “The Lyapunov Matrix Equation ,” Linear Algebra and Its Applications, Vol. 28, 1979, pp. 43-52. doi:10.1016/0024-3795(79)90117-4
- A. C. Antoulas and D. C.Sorensen, “Lyapunov, Lanczos and Inertia,” Linear Algebra and Its Applications, Vol. 326, No. 1-3, 2001, pp. 137-150. doi:10.1016/S0024-3795(00)00288-3
- D. Carlson and B. N. Datta, “On the Effective Computation of the Inertia of a Nonhermitian Matrix,” Numerical Mathematics, Vol. 33, No. 3, 1979, pp. 315-322. doi:10.1007/BF01398647
- B. N. Datta, “Stability and Inertia,” Linear Algebra and Its Applications, Vol. 302-303, 2000, pp. 563-600. doi:10.1016/S0024-3795(99)00213-X