On the Uniform Asymptotic Stability of Certain Linear Non-Autonomous Differential Equations

Download or read book On the Uniform Asymptotic Stability of Certain Linear Non-Autonomous Differential Equations written by A. P. Morgan and published by . This book was released on 1975 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ordinary differential equation dx/dt = -P(t)x where P(t) 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 x(t) 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 P(t) 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.