A switching control approach for linear systems subject to asymmetric actuator saturation

In this paper, we study the saturation control problem for linear time-invariant (LTI) systems subject to asymmetric actuator saturation under a switching control framework. The LTI plant with asymmetric saturation is first transformed to an equivalent switched linear model with each subsystem subject to symmetric actuator saturation, based on which a switching controller robust against arbitrary switching is then designed by using a common Lyapunov function approach. The controller synthesis conditions are formulated in terms of linear matrix inequalities (LMIs). The application to an inverted pendulum is also given to illustrate the effectiveness and advantages of the proposed approach.

[1]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[2]  Faryar Jabbari,et al.  Output feedback controllers for disturbance attenuation with actuator amplitude and rate saturation , 2000, Autom..

[3]  Zongli Lin,et al.  Disturbance attenuation by output feedback for linear systems subject to actuator saturation , 2009 .

[4]  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).

[5]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[6]  Sophie Tarbouriech,et al.  Control of Uncertain Systems with Bounded Inputs , 1997 .

[7]  Wilson J. Rugh,et al.  Research on gain scheduling , 2000, Autom..

[8]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

[9]  Fen Wu.  New results on output feedback disturbance attenuation of saturated linear systems , 2011, Proceedings of the 30th Chinese Control Conference.

[10]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[11]  Tingshu Hu,et al.  On semiglobal stabilizability of antistable systems by saturated linear feedback , 2002, IEEE Trans. Autom. Control..

[12]  Luca Zaccarian,et al.  Output feedback design for saturated linear plants using deadzone loops , 2009, Autom..

[13]  Luca Zaccarian,et al.  Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions , 2006, IEEE Transactions on Automatic Control.

[14]  S. Żak.  Systems and control , 2002 .

[15]  Zongli Lin,et al.  Low gain feedback , 1999 .

[16]  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).

[17]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[18]  Tingshu Hu,et al.  Null controllability and stabilization of linear systems subject to asymmetric actuator saturation , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).