Robustness of Global Exponential Stability of Nonlinear Systems With Random Disturbances and Time Delays
研究了受时滞和随机扰动影响的非线性系统保持指数稳定性的条件，给出了允许的时滞和噪声强度的上界，并通过数值例子验证了结果的有效性。
The robust stability of nonlinear systems has been studied extensively. It is well known that time delays and additive noises may derail the stability of nonlinear systems. This paper presents theoretical results on the robustness of the exponential stability of nonlinear systems in the presence of time delays and random disturbances. For a given exponentially stable (ES) nonlinear system, it is interesting to know how much time delay and noise intensity there are so that the system may remain to be ES when the system is subject to delay and noise. Upper bounds of allowable delays and noise intensities are derived for nonlinear systems to keep their exponential stability. It is proven that if the noise and delay of ES nonlinear systems are lower than the upper bounds derived herein, the nonlinear systems infected by noises and delays are ensured to be ES. Three numerical examples are given to substantiate the efficacy of the results.