Stability analysis for linear discrete-time systems subject to actuator saturation

In this paper, stability of discrete-time linear systems subject to actuator saturation is analyzed by combining the saturation-dependent Lyapunov function method with Finsler’s lemma. New stability test conditions are proposed in the enlarged space containing both the state and its time difference which allow extra degree of freedom and lead to less conservative estimation of the domain of attraction. Furthermore, based on this result, a useful lemma and an iterative LMI-based optimization algorithm are also developed to maximize an estimation of domain of attraction. A numerical example illustrates the effectiveness of the proposed methods.

[1]  Tingshu Hu,et al.  Analysis of linear systems in the presence of actuator saturation and I-disturbances , 2004, Autom..

[2]  Claudio De Persis,et al.  Proceedings of the 41st IEEE Conference on Decision and Control , 2002 .

[3]  Tingshu Hu,et al.  Analysis and design for discrete-time linear systems subject to actuator saturation , 2002, Syst. Control. Lett..

[4]  Tingshu Hu,et al.  Analysis of linear systems in the presence of actuator saturation and L/sub 2/-disturbances , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[5]  Sophie Tarbouriech,et al.  Antiwindup design with guaranteed regions of stability: an LMI-based approach , 2005, IEEE Transactions on Automatic Control.

[6]  Stephen P. Boyd,et al.  Analysis of linear systems with saturation using convex optimization , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[7]  Faryar Jabbari,et al.  Disturbance attenuation for systems with input saturation: An LMI approach , 1999, IEEE Trans. Autom. Control..

[8]  S. Tarbouriech,et al.  Control design for linear systems with saturating actuators and /spl Lscr//sub 2/-bounded disturbances , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  Zongli Lin,et al.  Output Feedback Stabilization of Linear Systems With Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[10]  Karolos M. Grigoriadis,et al.  Actuator saturation control , 2002 .

[11]  Zongli Lin,et al.  Stability analysis of discrete-time systems with actuator saturation by a saturation-dependent Lyapunov function , 2003, Autom..

[12]  Michel Verhaegen,et al.  Proceedings of the 37th IEEE Conference on Decision and Control , 1998 .

[13]  Tetsuya Iwasaki,et al.  State Space Region Attaining L2 Performance for Saturating Control System , 2001 .

[14]  Tingshu Hu,et al.  Conjugate Lyapunov functions for saturated linear systems , 2005, Autom..