This note considers the stability of linear time varying second order systems. It studies the case where the stiffness matrix is a function of time. It provides sufficient conditions for stability and asymptotic stability of the system provided that certain conditions on the stiffness matrix are satisfied.

1.
Müller
,
P. C.
, and
Schiehlen
,
W. O.
, 1985,
Linear Vibrations
,
Martinus Nijhoff
,
Dordrecht, Netherlands
.
2.
D’Angelo
,
H.
, 1970,
Linear Time-Varying Systems: Analysis and Synthesis
,
Allyn and Bacon
,
Boston
.
3.
Hsu
,
P.
, and
Wu
,
J. W.
, 1991, “
Stability of Second-Order Multidimensional Linear Time Varying Systems
,”
J. Guid. Control Dyn.
0731-5090,
14
(
5
), pp.
1040
1045
.
4.
Shrivastava
,
S. K.
, and
Pradeep
,
S.
, 1985, “
Stability of Multidimensional Linear Time Varying Systems
,”
J. Guid. Control Dyn.
0731-5090,
8
(
5
), pp.
579
583
.
5.
Wu
,
J. W.
, and
Fung
,
R. F.
, 1999, “
On Stability of Time Varying Multidimensional Linear Systems
,”
J. Geophys. Res.
0148-0227,
121
, pp.
509
511
.
6.
Gil’
,
M. I.
, 1998,
Stability of Finite and Infinite Dimensional Systems
,
Kluwer
,
Boston
.
7.
Willems
,
J. L.
, 1970,
Stability Theory of Dynamical Systems
,
Wiley
,
New York
.
8.
Coppel
,
W. A.
, 1965,
Stability and Asymptotic Behavior of Differential Equations
,
D. C. Heath
,
Boston
.
9.
Slotine
,
J. J. E.
, and
Li
,
W.
, 1991,
Applied Nonlinear Control
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
10.
Shahruz
,
S. M.
, 2000, “
Discussion on Stability of Time Varying Multidimensional Linear Systems
,”
ASME J. Vibr. Acoust.
0739-3717,
122
, pp.
337
338
.
You do not currently have access to this content.