Global stabilisation of high-order nonlinear systems with multiple time delays

This paper focuses on the stabilisation for a class of high-order nonlinear systems with multiple time delays. Growth restriction on system nonlinearities is further relaxed. Design procedures of a continuous controller are provided by the method of adding a power integrator, and the stability of the resulting closed-loop system is rigorously proven with the help of the elegant choice of a Lyapunov–Krasovskii functional. Finally, a simulation example is provided to demonstrate the validness of the proposed approach.

[1]  Nahum Shimkin,et al.  Nonlinear Control Systems , 2008 .

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

[3]  Zhong-Ping Jiang,et al.  A small-gain condition for iISS of interconnected retarded systems based on Lyapunov-Krasovskii functionals , 2010, Autom..

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

[5]  Yungang Liu,et al.  Adaptive Practical Output Tracking Control for High-order Nonlinear Uncertain Systems , 2008 .

[6]  Yungang Liu,et al.  GLOBAL STABILIZATION FOR A CLASS OF HIGH-ORDER TIME-DELAY NONLINEAR SYSTEMS , 2011 .

[7]  Wei Lin,et al.  Practical output tracking of nonlinear systems with uncontrollable unstable linearization , 2002, IEEE Trans. Autom. Control..

[8]  Tielong Shen,et al.  Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach , 2005, IEEE Transactions on Automatic Control.

[9]  Gang Feng,et al.  Robust controller design of a class of nonlinear time delay systems via backstepping method , 2008, Autom..

[10]  P. Pepe,et al.  A Lyapunov-Krasovskii methodology for ISS and iISS of time-delay systems , 2006, Syst. Control. Lett..

[11]  Zong-Yao Sun.  Adaptive Practical Output Tracking Control for High-order Nonlinear Uncertain Systems: Adaptive Practical Output Tracking Control for High-order Nonlinear Uncertain Systems , 2009 .

[12]  YunGang Liu,et al.  Global Practical Tracking for High-Order Uncertain Nonlinear Systems with Unknown Control Directions , 2010, SIAM J. Control. Optim..

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

[14]  Jean-Pierre Richard,et al.  Time-delay systems: an overview of some recent advances and open problems , 2003, Autom..

[15]  Wei Lin,et al.  Nonsmooth adaptive stabilization of cascade systems with nonlinear parameterization via partial-state feedback , 2003, IEEE Trans. Autom. Control..

[16]  Wei Lin,et al.  Adaptive output tracking of inherently nonlinear systems with nonlinear parameterization , 2003, IEEE Trans. Autom. Control..

[17]  Shuzhi Sam Ge,et al.  Adaptive neural network control of nonlinear systems with unknown time delays , 2003, IEEE Trans. Autom. Control..

[18]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: the smooth feedback case , 2002, IEEE Trans. Autom. Control..

[19]  L. Baron,et al.  Asymptotic stabilization of high‐order feedforward systems with delays in the input , 2010 .

[20]  Yungang Liu,et al.  Adaptive stabilisation for a large class of high-order uncertain non-linear systems , 2009, Int. J. Control.

[21]  Frédéric Mazenc,et al.  Backstepping design for time-delay nonlinear systems , 2006, IEEE Transactions on Automatic Control.

[22]  P. Olver.  Nonlinear Systems , 2013 .

[23]  Jianhong Wu,et al.  Introduction to Functional Differential Equations , 2013 .

[24]  Luc Baron,et al.  Feedback stabilization for high order feedforward nonlinear time-delay systems , 2011, Autom..

[25]  Junmin Li,et al.  Adaptive neural control for a class of nonlinearly parametric time-delay systems , 2005, IEEE Transactions on Neural Networks.

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

[27]  Zongli Lin,et al.  On Input-to-State Stability for Nonlinear Systems with Delayed Feedbacks , 2007, ACC.

[28]  Peng Shi,et al.  Robust backstepping control for a class of time delayed systems , 2005, IEEE Transactions on Automatic Control.

[29]  Tielong Shen,et al.  Further Result on Robust Stabilization for Uncertain Nonlinear Time-delay Systems , 2007 .

[30]  Yungang Liu,et al.  Adaptive state-feedback stabilization for a class of high-order nonlinear uncertain systems , 2007, Autom..

[31]  Qing-Chang Zhong,et al.  Robust Control of Time-delay Systems , 2006 .

[32]  Miroslav Krstic,et al.  Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.