Stability of matrix second-order systems: new conditions and perspectives

Author

Diwekar, Anjali M. ; Yedavalli, Rama K.

Author_Institution

Dept. of Aerospace Eng., Appl. Mech. & Aviation, Ohio State Univ., Columbus, OH, USA

Volume

44

Issue

9

fYear

1999

fDate

9/1/1999 12:00:00 AM

Firstpage

1773

Lastpage

1777

Abstract

Modeling of many dynamic systems results in matrix second-order differential equations. In the paper, the stability issues of matrix second-order dynamical systems are discussed. In the literature, only sufficient conditions of stability and/or instability for a system in matrix second-order form are available. In this paper, necessary and sufficient conditions of asymptotic stability for time-invariant systems in matrix second-order form under different types of dynamic loadings (conservative/nonconservative) are derived and a physical interpretation is carried out. The stability conditions in the sense of Lyapunov (the jw-axis behavior of eigenvalues) are also analyzed. As the conditions are gained directly in terms of physical parameters of the system, the effect of different loadings on the system stability is made transparent by dealing with the stability issues directly in matrix second-order form

Keywords

Lyapunov methods; asymptotic stability; differential equations; matrix algebra; stability criteria; dynamic loadings; dynamic systems; matrix second-order differential equations; matrix second-order systems; necessary and sufficient conditions; stability conditions; time-invariant systems; Automatic control; Control systems; Controllability; Eigenvalues and eigenfunctions; Linear algebra; Observability; Robust control; Robust stability; Robustness; Sufficient conditions;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.788551

Filename

788551