Noise-to-state stability analysis for a class of random time-delay nonlinear systems

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.

[1]  Zhaojing Wu,et al.  Stability Criteria of Random Nonlinear Systems and Their Applications , 2015, IEEE Transactions on Automatic Control.

[2]  Liang Liu,et al.  Asymptotic stabilization of stochastic high-order upper-triangular nonlinear systems with input time-varying delay , 2017 .

[3]  Hangli Ren,et al.  Robust input‐output finite‐time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities , 2017 .

[4]  Luc Baron,et al.  Design of Stabilizing Controllers With a Dynamic Gain for Feedforward Nonlinear Time-Delay Systems , 2011, IEEE Transactions on Automatic Control.

[5]  Shengyuan Xu,et al.  Further results on output-feedback stabilization of stochastic upper-triangular systems with state and input time-delays , 2018 .

[6]  Liang Liu,et al.  State feedback stabilization for stochastic feedforward nonlinear systems with time-varying delay , 2013, Autom..

[7]  Shengyuan Xu,et al.  Stability analysis for a class of random nonlinear impulsive systems , 2017 .

[8]  Shuzhi Sam Ge,et al.  Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays , 2008, Int. J. Control.

[9]  W. Zheng,et al.  Finite‐time H ∞  control for discrete‐time switched nonlinear systems with time delay , 2015 .

[10]  Liangjian Hu,et al.  Delay dependent stability of highly nonlinear hybrid stochastic systems , 2017, Autom..

[11]  Qian Ma,et al.  State feedback control for a class of stochastic high-order feedforward nonlinear systems with time-varying delays: a homogeneous domination approach , 2014 .

[12]  Kai Liu.  Stochastic Stability of Differential Equations in Abstract Spaces , 2022 .

[13]  X. Mao,et al.  Stochastic Differential Equations and Applications , 1998 .

[14]  Yang Tang,et al.  Input-to-state stability of impulsive stochastic delayed systems under linear assumptions , 2016, Autom..

[15]  Yuqiang Wu,et al.  Observer-based finite-time exponential l2 − l∞ control for discrete-time switched delay systems with uncertainties , 2013 .

[16]  Yuanqing Xia,et al.  Noise-to-State Stability of Random Switched Systems and Its Applications , 2016, IEEE Transactions on Automatic Control.

[17]  Jinde Cao,et al.  Robust Exponential Stability of Markovian Jump Impulsive Stochastic Cohen-Grossberg Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[18]  Shengyuan Xu,et al.  On Stability of a Class of Switched Nonlinear Systems Subject to Random Disturbances , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Yi Shen,et al.  Stability and boundedness of nonlinear hybrid stochastic differential delay equations , 2013, Syst. Control. Lett..

[20]  Hangli Ren,et al.  Finite-time stability of interconnected impulsive switched systems , 2015, 2015 34th Chinese Control Conference (CCC).

[21]  Huanqing Wang,et al.  Global asymptotic stabilization of stochastic feedforward nonlinear systems with input time-delay , 2015, Nonlinear Dynamics.

[22]  Jinde Cao,et al.  Exponential Stability of Stochastic Neural Networks With Both Markovian Jump Parameters and Mixed Time Delays , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[23]  Guangdeng Zong,et al.  Finite-time stochastic input-to-state stability of impulsive switched stochastic nonlinear systems , 2014, CCC 2014.

[24]  Huaguang Zhang,et al.  Global Asymptotic Stability and Stabilization of Neural Networks With General Noise , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[25]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .