Global state feedback stabilization of high-order nonlinear systems with multiple time-varying delays

Abstract This paper studies the global stabilization problem for a class of high-order nonlinear systems with low-order and high-order nonlinearities, and multiple time-varying delays. Systems become more general due to both low-order and high-order in nonlinearities taking values in certain intervals. By introducing a novel Lyapunov–Krasovskii functional, a state feedback controller based on the Lyapunov–Krasviskii theorem together with the adding a power integrator and sign function methods is designed to guarantee the globally uniformly asymptotic stability of the closed-loop system.

[1]  R. Marino,et al.  Dynamic output feedback linearization and global stabilization , 1991 .

[2]  Xin Yu,et al.  Corrections to “Stochastic Barbalat's Lemma and Its Applications” [Jun 12 1537-1543] , 2014, IEEE Transactions on Automatic Control.

[3]  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.

[4]  H. Khalil,et al.  Adaptive stabilization of a class of nonlinear systems using high-gain feedback , 1987 .

[5]  C. Qian,et al.  A generalized homogeneous domination approach for global stabilization of inherently nonlinear systems via output feedback , 2007 .

[6]  Xue-Jun Xie,et al.  Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable , 2009, Autom..

[7]  Peng Shi,et al.  Backstepping Control in Vector Form for Stochastic Hamiltonian Systems , 2012, SIAM J. Control. Optim..

[8]  Cong-Ran Zhao,et al.  Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay , 2014, Autom..

[9]  Wei Lin,et al.  TAKING ADVANTAGE OF HOMOGENEITY: A UNIFIED FRAMEWORK FOR OUTPUT FEEDBACK CONTROL OF NONLINEAR SYSTEMS , 2007 .

[10]  Wei Lin,et al.  Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm , 2002, IEEE Trans. Autom. Control..

[11]  Jie Tian,et al.  Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization , 2009, Autom..

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

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

[14]  Peng Shi,et al.  Modeling and adaptive tracking for a class of stochastic Lagrangian control systems , 2013, Autom..

[15]  Xue-Jun Xie,et al.  Output Tracking of High-Order Stochastic Nonlinear Systems with Application to Benchmark Mechanical System , 2010, IEEE Transactions on Automatic Control.

[16]  Ji Li,et al.  A dual‐observer design for global output feedback stabilization of nonlinear systems with low‐order and high‐order nonlinearities , 2009 .

[17]  Wuquan Li,et al.  Output Tracking of Stochastic High-Order Nonlinear Systems with Markovian Switching , 2013, IEEE Transactions on Automatic Control.

[18]  Wei Lin,et al.  A Dual Observer Method for Global Stabilization of Nonlinear Systems with Limited and Uncertain Information , 2007, 2007 American Control Conference.

[19]  Hao Lei.  Universal Output Feedback Control of Nonlinear Systems , 2008 .

[20]  Yuanqing Xia,et al.  Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching , 2008, 2008 27th Chinese Control Conference.

[21]  Yuanqing Xia,et al.  Stochastic Barbalat's Lemma and Its Applications , 2012, IEEE Transactions on Automatic Control.

[22]  Wei Lin,et al.  Reduced-order observer, homogeneous domination and nonsmooth output feedback stabilization of nonlinear systems , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[23]  Mingyue Cui,et al.  Output feedback tracking control of stochastic Lagrangian systems and its application , 2014, Autom..

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

[25]  Hao Lei,et al.  Robust Control of Uncertain Nonlinear Systems by Output Feedback , 2007, 2007 American Control Conference.

[26]  Cong-Ran Zhao,et al.  A Combined Homogeneous Domination and Sign Function Approach to Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems , 2014, IEEE Transactions on Automatic Control.

[27]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[28]  Xin Yu,et al.  Output Feedback Regulation of Stochastic Nonlinear Systems With Stochastic iISS Inverse Dynamics , 2010, IEEE Transactions on Automatic Control.

[29]  Chunjiang Qian,et al.  A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[30]  Sing Kiong Nguang,et al.  Robust stabilization of a class of time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[31]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[32]  Liang Liu,et al.  Decentralized adaptive stabilization for interconnected systems with dynamic input-output and nonlinear interactions , 2010, Autom..

[33]  Wei Lin,et al.  Recursive Observer Design, Homogeneous Approximation, and Nonsmooth Output Feedback Stabilization of Nonlinear Systems , 2006, IEEE Transactions on Automatic Control.

[34]  Hamid Reza Karimi,et al.  Stability of Stochastic Nonlinear Systems With State-Dependent Switching , 2013, IEEE Transactions on Automatic Control.

[35]  I. Kolmanovsky,et al.  Nonsmooth stabilization of an underactuated unstable two degrees of freedom mechanical system , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[36]  C. Qian,et al.  A Generalized Framework for Global Output Feedback Stabilization of Genuinely Nonlinear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[37]  Yuanqing Xia,et al.  Exponential stability for stochastic systems with hysteresis switching , 2012, Proceedings of the 31st Chinese Control Conference.

[38]  Mingyue Cui,et al.  Dynamics Modeling and Tracking Control of Robot Manipulators in Random Vibration Environment , 2013, IEEE Transactions on Automatic Control.

[39]  Xinghui Zhang,et al.  Continuous global stabilisation of high-order time-delay nonlinear systems ++ , 2013, Int. J. Control.

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

[41]  Xue-Jun Xie,et al.  Output-Feedback Stabilization of Stochastic High-Order Nonlinear Systems under Weaker Conditions , 2011, SIAM J. Control. Optim..

[42]  Chunjiang Qian,et al.  Global Output Feedback Stabilization of a Class of Nonlinear Systems via Linear Sampled-Data Control , 2012, IEEE Transactions on Automatic Control.

[43]  Peter Xiaoping Liu,et al.  Backstepping Control for Nonlinear Systems With Time Delays and Applications to Chemical Reactor Systems , 2009, IEEE Transactions on Industrial Electronics.

[44]  Xue-Jun Xie,et al.  Output-feedback control of a class of high-order stochastic nonlinear systems , 2009, Int. J. Control.

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

[46]  Riccardo Marino,et al.  Output Feedback Control of a Class Of Nonlinear Systems , 1992 .

[47]  Xue-Jun Xie,et al.  Further Results on Output-Feedback Stabilization for a Class of Stochastic Nonlinear Systems , 2011, IEEE Transactions on Automatic Control.

[48]  J. Tsinias.  A theorem on global stabilization of nonlinear systems by linear feedback , 1991 .

[49]  MingQing Xiao,et al.  Nonlinear Observer Design in the Siegel Domain , 2002, SIAM J. Control. Optim..

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

[51]  Zhen-Guo Liu,et al.  Global stabilisation of high-order nonlinear systems with multiple time delays , 2013, Int. J. Control.

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

[53]  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.

[54]  Ji Li,et al.  Global Finite-Time Stabilization of a Class of Uncertain Nonlinear Systems Using Output Feedback , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[55]  Wei Lin,et al.  Smooth Feedback, Global Stabilization, and Disturbance Attenuation of Nonlinear Systems with Uncontrollable Linearization , 2001, SIAM J. Control. Optim..

[56]  Peng Shi,et al.  Adaptive Tracking for Stochastic Nonlinear Systems With Markovian Switching $ $ , 2010, IEEE Transactions on Automatic Control.

[57]  Peng Shi,et al.  Theory of Stochastic Dissipative Systems , 2011, IEEE Transactions on Automatic Control.