On the Uniform Asymptotic Stability of Certain Linear Non-Autonomous Differential Equations.
YALE UNIV NEW HAVEN CONN BECTON CENTER
Pagination or Media Count:
The ordinary differential equation dxdt -Ptx where Pt is symmetric positive semi-definite time-varying matrix arises often in mathematical control theory. In this paper the authors consider the stability properties in the sense of Lyapunov of the equilibrium state xt identically equal to 0. It is a relatively trivial exercise to show that the origin is stable but uniform asymptotic stability does not generally hold unless Pt is positive definite. The semi-definite case arises much more frequently in practice than the definite one and the main effort in this paper is directed towards finding conditions implying uniform asymptotic stability in such a case.
- Theoretical Mathematics