Exponential Stability For Linear Time-Varying Differential Systems With Constant Delay

In this paper we discuss the stability problem of the one-dimensional linear delay-differential equation and the two-dimensional linear time-varying differential system,it is one of typical problem in the stability study of the delay-differential equation.Firstly,we establish some sufficient conditions under which the zero solution of the one-dimensional linear delaydifferential equation is uniformly stable and exponentially stable,respectively.Where the coefficient is in the form of the sum of a constant and a function,and we do not necessarily assume that the coefficient is positive on the domain [0,∞).In this case we improve the stability theorem in [1].Secondly,we consider the two-dimensional linear time-varying differential system.Where the 2×2 matrix included in the system satisfying with|θ| <π/2.We give some sufficient conditions for the exponential stability of the above differential system.