Stability of Delayed Homogeneous Positive Differential–Difference Systems

Abstract

Stability theory of linear differential-difference system has been well-established, while fewer results can be found for nonlinear differential-difference systems. In this paper, stability and boundedness of homogeneous differential-difference system with bounded delay is studied based on the system positivity. At first, an exponential stability criterion is obtained, which is an extension of an existing result. Next, another boundary is computed under the previous condition, which proves to be tighter than the first result at least in some cases. Then a finite-time stability condition is achieved for the delay-free system, and an upper bound of the settling time and an explicit boundary of the state are derived. Finally, a numerical example is given to verify the results presented in this paper.