Integral Sliding Mode Control for a Class of Uncertain Switched Nonlinear Systems

In this paper, a new integral sliding mode control scheme is proposed for a class of uncertain switched nonlinear systems. First, a nonlinear integral sliding surface is constructed such that the switched system under the sliding mode is exponentially stable for switching laws with an average dwell time switching property. Then, variable structure controllers are designed to guarantee the existence of the sliding mode from the initial time. Robustness of the closed-loop system in the whole state space is obtained. Finally, a numerical example is given to illustrate the effectiveness of the proposed design method.

[1]  Long Wang,et al.  Linear matrix inequality approach to quadratic stabilisation of switched systems , 2004 .

[2]  Han Ho Choi,et al.  LMI-Based Sliding Surface Design for Integral Sliding Mode Control of Mismatched Uncertain Systems , 2007, IEEE Transactions on Automatic Control.

[3]  Guangming Xie,et al.  Quadratic stabilization of switched systems , 2005, Int. J. Syst. Sci..

[4]  Alberto L. Sangiovanni-Vincentelli,et al.  Hybrid control in automotive applications: the cut-off control , 1999, Autom..

[5]  H. Hirai,et al.  A mode-switching control for motion control and its application to disk drives: design of optimal mode-switching conditions , 1998 .

[6]  Daizhan Cheng,et al.  On quadratic Lyapunov functions , 2003, IEEE Trans. Autom. Control..

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

[8]  Han Ho Choi,et al.  An LMI-based switching surface design method for a class of mismatched uncertain systems , 2003, IEEE Trans. Autom. Control..

[9]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[10]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[11]  V. Utkin,et al.  Integral sliding mode in systems operating under uncertainty conditions , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[12]  Masayoshi Tomizuka,et al.  Learning hybrid force and position control of robot manipulators , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[13]  Zhendong Sun.  A robust stabilizing law for switched linear systems , 2004 .

[14]  V. Utkin.  Variable structure systems with sliding modes , 1977 .

[15]  I. Petersen.  A stabilization algorithm for a class of uncertain linear systems , 1987 .

[16]  Kyung-Soo Kim,et al.  Designing robust sliding hyperplanes for parametric uncertain systems: a Riccati approach , 2000, Autom..

[17]  João Pedro Hespanha,et al.  Switching between stabilizing controllers , 2002, Autom..

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

[19]  A. Morse.  Supervisory control of families of linear set-point controllers Part I. Exact matching , 1996, IEEE Trans. Autom. Control..

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

[21]  Guangming Xie,et al.  Controllability and stabilizability of switched linear-systems , 2003, Syst. Control. Lett..

[22]  A. Michel,et al.  Stability theory for hybrid dynamical systems , 1998, IEEE Trans. Autom. Control..

[23]  R. Decarlo,et al.  Asymptotic Stability of m-Switched Systems using Lyapunov-Like Functions , 1991, 1991 American Control Conference.

[24]  Shuzhi Sam Ge,et al.  Controllability and reachability criteria for switched linear systems , 2002, Autom..

[25]  Daniel Liberzon,et al.  Benchmark Problems in Stability and Design of Switched Systems , 1999 .

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

[27]  K. Narendra,et al.  A common Lyapunov function for stable LTI systems with commuting A-matrices , 1994, IEEE Trans. Autom. Control..

[28]  Jian-Xin Xu,et al.  Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems , 2004, IEEE Transactions on Automatic Control.

[29]  A. Michel,et al.  PIECEWISE LYAPUNOV FUNCTIONS FOR SWITCHED SYSTEMS WITH AVERAGE DWELL TIME , 2000 .

[30]  Jun Zhao,et al.  Hybrid control for global stabilization of the cart-pendulum system , 2001, Autom..