Dynamic State Feedback Stabilization of Stochastic Cascade Nonlinear Time-Delay Systems With SISS Inverse Dynamics

This paper investigates state feedback stabilization problem of a class of stochastic cascade nonlinear time-delay systems with stochastic inverse dynamics. By characterizing unmeasured stochastic inverse dynamics with stochastic input-to-state stability condition, without imposing any growth condition on time-delay system nonlinearities, a delay-independent, dynamic state feedback controller is constructed. It is shown that the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability.

[1]  W. Marsden.  I and J , 2012 .

[2]  Hongmin Li,et al.  Fuzzy-Approximation-Based Adaptive Output-Feedback Control for Uncertain Nonsmooth Nonlinear Systems , 2018, IEEE Transactions on Fuzzy Systems.

[3]  Liang Liu,et al.  Output-feedback stabilization for stochastic high-order nonlinear systems with time-varying delay , 2011, Autom..

[4]  Xue-Jun Xie,et al.  Adaptive backstepping controller design using stochastic small-gain theorem , 2007, Autom..

[5]  Xin Yu,et al.  State-Feedback Control of High-Order Stochastic Nonlinear Systems with SiISS Inverse Dynamics , 2011, IEEE Transactions on Automatic Control.

[6]  Hiroshi Ito,et al.  An iISS Framework for Stochastic Robustness of Interconnected Nonlinear Systems , 2016, IEEE Transactions on Automatic Control.

[7]  Weisheng Chen,et al.  State‐feedback stabilization for a class of stochastic time‐delay nonlinear systems , 2012 .

[8]  Wei Lin,et al.  Dynamic partial state feedback control of cascade systems with time-delay , 2017, Autom..

[9]  Xin Yu,et al.  Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics , 2010, Autom..

[10]  Hiroshi Ito,et al.  Stability of stochastic nonlinear systems in cascade with not necessarily unbounded decay rates , 2015, Autom..

[11]  Liang Liu,et al.  Further results on output feedback stabilization for stochastic high-order nonlinear systems with time-varying delay , 2012, Autom..

[12]  Gang Feng,et al.  Robust adaptive output feedback control to a class of non-triangular stochastic nonlinear systems , 2018, Autom..

[13]  Eduardo Sontag,et al.  Changing supply functions in input/state stable systems , 1995, IEEE Trans. Autom. Control..

[14]  J. Tsinias.  Stochastic input-to-state stability and applications to global feedback stabilization , 1998 .

[15]  Zhong-Ping Jiang,et al.  Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems , 2007, Autom..

[16]  Guangdeng Zong,et al.  Adaptive Neural Tracking Control for Switched High-Order Stochastic Nonlinear Systems , 2017, IEEE Transactions on Cybernetics.

[17]  Wei Lin,et al.  A continuous feedback approach to global strong stabilization of nonlinear systems , 2001, IEEE Trans. Autom. Control..

[18]  Songjiao Shi,et al.  Output feedback stabilization for a class of stochastic time-delay nonlinear systems , 2003, IEEE Trans. Autom. Control..

[19]  Liang Liu,et al.  A Homogeneous Domination Approach to State Feedback of Stochastic High-Order Nonlinear Systems With Time-Varying Delay , 2013, IEEE Transactions on Automatic Control.

[20]  Ji-Feng Zhang,et al.  Global output-feedback stabilization for a class of stochastic non-minimum-phase nonlinear systems , 2008, Autom..

[21]  Cong-Ran Zhao,et al.  Output Feedback Stabilization Using Small-Gain Method and Reduced-Order Observer for Stochastic Nonlinear Systems , 2013, IEEE Transactions on Automatic Control.

[22]  T. Başar,et al.  Stochastic stability of singularly perturbed nonlinear systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).