Time-delay systems disturbed by white noise have been comprehensively modelled as stochastic functional differential equations in the existing literature. However, in some specific situations, they cannot always precisely describe the dynamic character of time-delay systems subject to non-white noise disturbances. In this paper, colour noises with finite two-order moments are introduced to time-delay systems (such systems are referred to as random ones). First, we present some general conditions to guarantee the existence and uniqueness of solutions to random time-delay systems. Next, in light of these results and the Lyapunov function approach, the noise-to-state stability and eλt-weighted integral noise-to-state stability are analysed, respectively. One example is given to illustrate the effectiveness of the obtained results.
GuKQChenJKharitonovVL (2003) Stability of Time-Delay Systems. New York, NY: Springer Science & Business Media.
4.
HouLLZongGDWuYQ (2013) Observer-based finite-time exponential - control for discrete-time switched delay systems with uncertainties. Transactions of the Institute of Measurement and Control35(3): 310–320.
5.
HuLJMaoXRShenY (2013) Stability and boundedness of nonlinear hybrid stochastic differential delay equations. Systems & Control Letters62(2): 178–187.
6.
JiaoTCCuiGZLuJWet al. (2014) State feedback control for a class of stochastic high-order feedforward nonlinear systems with time-varying delays: A homogeneous domination approach. Transactions of the Institute of Measurement and Control36(8): 1041–1050.
7.
JiaoTCZhengWXXuSY (2016) On stability of a class of switched nonlinear systems subject to random disturbances. IEEE Transactions on Circuits and Systems I: Regular Papers63(12): 2278–2289.
8.
JiaoTCZhengWXXuSY (2017) Stability analysis for a class of random nonlinear impulsive systems. International Journal of Robust and Nonlinear Control27(7): 1171–1193.
9.
KhasminskiiRZ (1980) Stochastic Stability of Differential Equations. Rockville, MD: S. N. International Publisher.
10.
LiuLXieXJ (2013) State-feedback stabilization for stochastic feedforward nonlinear systems with time-varying delay. Automatica49(4): 936–942.
11.
LiuLZhangYF (2017) Asymptotic stabilization of stochastic high-order upper-triangular nonlinear systems with input time-varying delay. Transactions of the Institute of Measurement and Control39(12): 1898–1905.
12.
LiuLLiXLWangHQ (2016) Global asymptotic stabilization of stochastic feedforward nonlinear systems with input time-delay. Nonlinear Dynamics83(3): 1503–1510.
13.
LiuLXuSYXieXJet al. (2017) Further results on output-feedback stabilization of stochastic upper-triangular systems with state and input time-delays. Transactions of the Institute of Measurement and Control. Epub online ahead of print 11 May 2017. DOI: 0142331217705947.
14.
LiuSJGeSSZhangJF (2008) Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays. International Journal of Control81(8): 1210–1220.
15.
MaoXR (2007) Stochastic Differential Equations and Applications. Amsterdam: Elsevier.
16.
RenHLZongGD (2017) Robust input-output finite-time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities. International Journal of Adaptive Control and Signal Processing31(10): 1437–1455.
17.
ShanQHZhangHGWangZSet al. (2016) Global asymptotic stability and stabilization of neural networks with general noise. IEEE Transactions on Neural Networks and Learning Systems. DOI: 10.1109/TNNLS.2016.2637567.
18.
WuXTTangYZhangWB (2016) Input-to-state stability of impulsive stochastic delayed systems under linear assumptions. Automatica66: 195–204.
19.
WuZJ (2015) Stability criteria of random nonlinear systems and their applications. IEEE Transactions on Automatic Control60(4): 1038–1049.
20.
ZhangHXiaYQWuZJ (2016) Noise-to-state stability of random switched systems and its applications. IEEE Transactions on Automatic Control61(6): 1607–1612.
21.
ZhangXFBaronLLiuQRet al. (2011) Design of stabilizing controllers with a dynamic gain for feedforward nonlinear time-delay systems. IEEE Transactions on Automatic Control56(3): 692–697.
22.
ZhuQXCaoJD (2010) Robust exponential stability of Markovian jump impulsive stochastic Cohen-Grossberg neural networks with mixed time delays. IEEE Transactions on Neural Networks21(8): 1314–1325.
23.
ZhuQXCaoJD (2011) Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)41(2): 341–353.
24.
ZongGDRenHLHouLL (2016) Finite-time stability of interconnected impulsive switched systems. IET Control Theory and Applications10(6): 648–654.
25.
ZongGDWangRHZhengWXet al. (2015) Finite-time control for discrete-time switched nonlinear systems with time delay. International Journal of Robust and Nonlinear Control25(6): 914–936.
