Stability Analysis Of Nonlinear Time-Varying Systems With Weak Lyapunov Form

In this paper we consider the uniform stability and the uniformly asymptotical stability of non-autonomous systems described by time-varying ordinary differential equations. It is very important both in theory and in application. After introducing the concept of integral manifold set, we discuss non-autonomous systems admitting a positive semi-definite time-varying Lyapunov function whose derivative is non-positive. Within the condition of uniform (asymptotical) stability with respect to a given integral manifold set, we give the condition which is sufficient to get the uniform (asymptotical) stability of the non-autonomous systems admitting a zero-state detectable additional condition. Our condition is general and practical which is proved by our examples.