Backstepping Robust H ∞ Control for a Class of Uncertain Switched Nonlinear Systems Under Arbitrary Switchings

This paper addresses global robust H ∞ control for a class of switched nonlinear systems with uncertainty under arbitrary switchings. Each subsystem is in lower triangular form. The uncertainties are assumed to be in a known compact set. The backstepping design technique is used to design a smooth state feedback controller that renders the associated closed‐loop switched system globally robustly asymptotically stable and imposes a pre‐specified upper bound to the L 2‐gain under arbitrary switchings. An example is provided to demonstrate the efficacy of the design approach.

[1]  A. Schaft,et al.  Nonlinear H ∞ almost disturbance decoupling , 1994 .

[2]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[3]  A. Isidori.  Global almost disturbance decoupling with stability for non minimum-phase single-input single-output , 1996 .

[4]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[5]  Ben M. Chen,et al.  Further results on almost disturbance decoupling with global asymptotic stability for nonlinear systems , 1999, Autom..

[6]  Lihua Xie,et al.  Global robust disturbance attenuation and almost disturbance decoupling for uncertain cascaded nonlinear systems , 1999, Autom..

[7]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

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

[9]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[10]  Guisheng Zhai,et al.  Stability and £ 2 Gain Analysis of Switched Symmetric Systems , 2003 .

[11]  Arthur Jutan,et al.  Almost disturbance decoupling of MIMO nonlinear systems and application to chemical processes , 2004, Autom..

[12]  D. Hill,et al.  Hybrid H∞ control based on multiple lyapunov functions , 2004 .

[13]  Zhijian Ji,et al.  Disturbance attenuation of uncertain switched linear systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  Lei Guo,et al.  STABILIZATION OF SWITCHED LINEAR SYSTEMS , 2003, IEEE Trans. Autom. Control..

[15]  Jun Zhao,et al.  H-infinity control for cascade minimum-phase switched nonlinear systems , 2005 .

[16]  S. Ge,et al.  Switched Linear Systems: Control and Design , 2005 .

[17]  Shuzhi Sam Ge,et al.  Switched Linear Systems , 2005 .

[18]  Michael Margaliot,et al.  Stability analysis of switched systems using variational principles: An introduction , 2006, Autom..

[19]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[20]  Jun Zhao,et al.  ROBUST FAULT‐TOLERANT CONTROL FOR A CLASS OF SWITCHED NONLINEAR SYSTEMS IN LOWER TRIANGULAR FORM , 2007 .

[21]  Liu Feng.  Stabilization of switched linear systems with bounded disturbances and unobservable switchings , 2007 .

[22]  Feng Liu.  Stabilization of switched linear systems with bounded disturbances and unobservable switchings , 2007, Science in China Series F: Information Sciences.

[23]  Guisheng Zhai,et al.  A Note on Multiple Lyapunov Functions and Stability Condition for Switched and Hybrid Systems , 2007, 2007 IEEE International Conference on Control Applications.

[24]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[25]  Jun Zhao,et al.  H∞ control for a class of non-minimum-phase cascade switched nonlinear systems , 2008, 2008 American Control Conference.

[26]  Jun Zhao,et al.  Control for a Class of Non-Minimum-Phase Cascade Switched Nonlinear Systems , 2008 .

[27]  Georgi M. Dimirovski,et al.  H∞ control for a class of cascade switched nonlinear systems , 2008 .

[28]  Zvi Artstein,et al.  On stabilization of switched linear systems , 2008, Syst. Control. Lett..

[29]  Jun Zhao,et al.  On stability, L 2 -gain and H 8 control for switched systems , 2008 .

[30]  Hai Lin,et al.  Stability and Stabilizability of Switched Linear Systems: A Survey of Recent Results , 2009, IEEE Transactions on Automatic Control.

[31]  Georgi M. Dimirovski,et al.  Stabilisation and L 2-gain analysis for a class of uncertain switched non-linear systems , 2009, Int. J. Syst. Sci..

[32]  Jenq-Lang Wu,et al.  Stabilizing controllers design for switched nonlinear systems in strict-feedback form , 2009, Autom..

[33]  Ming-Li Chiang,et al.  Variable structure adaptive backstepping control for a class of unknown switched linear systems , 2010, Proceedings of the 2010 American Control Conference.

[34]  Georgi M. Dimirovski,et al.  H∞ controller design for switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, 49th IEEE Conference on Decision and Control (CDC).

[35]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[36]  Jun Zhao,et al.  Backstepping H∞ control for switched nonlinear systems under arbitrary switchings , 2010, Proceedings of the 2010 American Control Conference.

[37]  Jong-Tae Lim,et al.  Global Regulation of a Class of Uncertain Nonlinear Systems by Switching Adaptive Controller , 2010, IEEE Transactions on Automatic Control.

[38]  Ben Niu,et al.  Stabilization and L 2 -gain analysis for a class of cascade switched nonlinear systems: An average dwell-time method , 2011 .

[39]  R. Guo,et al.  Stability analysis for a class of switched linear systems , 2012 .

[40]  Lei Chen,et al.  A critical review of the most popular types of neuro control , 2012 .