Global robust stabilisation of a class of uncertain switched nonlinear systems with dwell time specifications

This paper is concerned with the global robust stabilisation problem for a class of uncertain switched nonlinear systems in lower triangular form under any switching signal with dwell time specifications. The switched systems under consideration allow the uncertainties to appear in the system. We first design two classes of controllers containing a tuning gain. One designed by backstepping is related to a global convergence with respect to a compact set and the other with gain-scaling factor characters a local asymptotic stable toward the origin. A controller selection mechanism is then introduced to determine which class of controller is employed based on the compact set. The gain tuning mechanism related to the dwell time is then proposed to tune online the controller gain. It is shown that under our proposed control strategy, the global robust stability of the closed-loop switched system is achieved with the dwell time specifications. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

[1]  Patrizio Colaneri,et al.  H∞ and Dwell Time Specifications of Continuous-Time Switched Linear Systems , 2010 .

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

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

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

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

[6]  Daizhan Cheng,et al.  Control of switched linear systems with input saturation , 2010, Int. J. Syst. Sci..

[7]  José Luis Mancilla-Aguilar,et al.  Some results on the stabilization of switched systems , 2013, Autom..

[8]  P. Kokotovic,et al.  Adaptive nonlinear design with controller-identifier separation and swapping , 1995, IEEE Trans. Autom. Control..

[9]  Jun Zhao,et al.  Stabilization of switched nonlinear systems with passive and non-passive subsystems , 2012 .

[10]  Bin Jiang,et al.  Results and perspectives on fault tolerant control for a class of hybrid systems , 2011, Int. J. Control.

[11]  Shuzhi Sam Ge,et al.  Adaptive neural control for a class of switched nonlinear systems , 2009, Syst. Control. Lett..

[12]  Zhengrong Xiang,et al.  Stability analysis of switched systems under dynamical dwell time control approach , 2009, Int. J. Syst. Sci..

[13]  Peng Shi,et al.  Passivity and Passification for a Class of Uncertain Switched Stochastic Time-Delay Systems , 2013, IEEE Transactions on Cybernetics.

[14]  Jörg Raisch,et al.  Modal exact linearization of a class of second-order switched nonlinear systems , 2010 .

[15]  Global adaptive control of nonlinearly parametrized systems , 2003, IEEE Trans. Autom. Control..

[16]  Jong-Tae Lim,et al.  On Robust Approximate Feedback Linearization , 2004 .

[17]  Bin Jiang,et al.  On stabilization of switched nonlinear systems with unstable modes , 2009, Syst. Control. Lett..

[18]  Guisheng Zhai,et al.  On practical asymptotic stabilizability of switched affine systems , 2006 .

[19]  J.C. Geromel,et al.  ${\cal H}_\infty$ and Dwell Time Specifications of Continuous-Time Switched Linear Systems , 2010, IEEE Transactions on Automatic Control.

[20]  Panagiotis D. Christofides,et al.  Stabilization of nonlinear systems with state and control constraints using Lyapunov-based predictive control , 2005, Proceedings of the 2005, American Control Conference, 2005..

[21]  Long Wang,et al.  On stability of a class of switched nonlinear systems , 2013, Autom..

[22]  Uri Shaked,et al.  Robust stability and stabilization of linear switched systems with dwell time , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[23]  Patrizio Colaneri,et al.  A Nonconservative LMI Condition for Stability of Switched Systems With Guaranteed Dwell Time , 2012, IEEE Transactions on Automatic Control.

[24]  Zhao Jun,et al.  Global stabilization of a class of switched nonlinear systems under a pre-given switching law , 2012, Proceedings of the 31st Chinese Control Conference.

[25]  Panagiotis D. Christofides,et al.  Predictive control of switched nonlinear systems with scheduled mode transitions , 2005, IEEE Transactions on Automatic Control.

[26]  Bo Wang,et al.  L 2-gain analysis for networked predictive control systems based on switching method , 2009, Int. J. Control.

[27]  Shuzhi Sam Ge,et al.  Analysis and synthesis of switched linear control systems , 2005, Autom..

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

[29]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

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

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

[32]  Andres Lopez,et al.  An equivalent continuous model for switched systems , 2013, Syst. Control. Lett..

[33]  Alessandro Pisano,et al.  Switched Observers for Switched Linear Systems With Unknown Inputs , 2011, IEEE Transactions on Automatic Control.

[34]  Peter Kuster,et al.  Nonlinear And Adaptive Control Design , 2016 .

[35]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

[36]  Wei Xing Zheng,et al.  Weighted H∞ model reduction for linear switched systems with time-varying delay , 2009, Autom..

[37]  Cong Wang,et al.  Dissipativity-based switching adaptive control , 2011, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.