State feedback stabilization for a class of nonlinear time-delay systems via dynamic linear controllers

The dynamic linear state feedback control problem is addressed for a class of nonlinear systems subject to time-delay. First, using the dynamic change of coordinates, the problem of global state feedback stabilization is solved for a class of time-delay systems under a type of nonhomogeneous growth conditions. With the aid of an appropriate Lyapunov-Krasovskii functional and the adaptive strategy used in coordinates, the closed-loop system can be globally asymptotically stabilized by the dynamic linear state feedback controller. The growth condition in perturbations are more general than that in the existing results. The correctness of the theoretical results are illustrated with an academic simulation example.

[1]  Qi Li,et al.  Global uniform asymptotical stability of a class of nonlinear cascaded systems with application to a nonholonomic wheeled mobile robot , 2010, Int. J. Syst. Sci..

[2]  Yungang Liu,et al.  State-feedback stabilization control design for a class of time-delay high-order nonlinear systems , 2011, Proceedings of the 30th Chinese Control Conference.

[3]  Orest Iftime,et al.  Proceedings of the 16th IFAC World congress , 2006 .

[4]  Alessandro Astolfi,et al.  Homogeneous Approximation, Recursive Observer Design, and Output Feedback , 2008, SIAM J. Control. Optim..

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

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

[7]  Chunjiang Qian,et al.  Semi-global stabilization of a class of uncertain nonlinear systems by linear output feedback , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[8]  Wei Lin,et al.  UNIVERSAL OUTPUT FEEDBACK CONTROL OF NONLINEAR SYSTEMS WITH UNKNOWN GROWTH RATE , 2005 .

[9]  van der Arjan Schaft,et al.  Proceedings of the 44th IEEE Conference on Decision and Control, and European Control Conference, 2005 , 2005 .

[10]  Wei Lin,et al.  Adaptive control of nonlinearly parameterized systems: a nonsmooth feedback framework , 2002, IEEE Trans. Autom. Control..

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

[12]  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..

[13]  Wei-Sung Lin,et al.  A Universal Control Approach for a Family of Uncertain Nonlinear Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[14]  Wei Lin,et al.  Robust control of uncertain systems with polynomial nonlinearity by output feedback , 2009 .

[15]  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.