On IQC Approach to the Analysis and Design of Linear Systems Subject to Actuator Saturation

This paper establishes IQC (integral quadratic constraints) based conditions under which an ellipsoid is contractively invariant for a single input linear system under a saturated linear feedback law. Based on these set invariance conditions, the determination of the largest such ellipsoid, for use as an estimate of the domain of attraction, can be formulated and solved as an LMI optimization problem. Such an LMI problem can also be readily adapted for the design of the feedback gain that achieves the largest contractively invariant ellipsoid. While the advantages of the proposed IQC approach remain to be explored, it is shown in this paper that the largest contractively invariant ellipsoid determined by this approach is the same as the one determined by the existing approach based on expressing the saturated linear feedback as a linear differential inclusion (LDI), which is known to lead to non-conservative result in determining the largest contractively invariant ellipsoid for single input systems

[1]  Dragan Nesic,et al.  Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005 , 2005, CDC 2005.

[2]  Tingshu Hu,et al.  Exact characterization of invariant ellipsoids for single input linear systems subject to actuator saturation , 2002, IEEE Trans. Autom. Control..

[3]  Tingshu Hu,et al.  Absolute stability with a generalized sector condition , 2004, IEEE Transactions on Automatic Control.

[4]  A. Rantzer,et al.  System analysis via integral quadratic constraints , 1997, IEEE Trans. Autom. Control..

[5]  Sophie Tarbouriech,et al.  Stability regions for linear systems with saturating controls via circle and Popov criteria , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[6]  Tingshu Hu,et al.  Exact characterization of invariant ellipsoids for linear systems with saturating actuators , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[8]  Alexandre Megretski,et al.  New results for analysis of systems with repeated nonlinearities , 2001, Autom..

[9]  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).

[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]  Franco Blanchini,et al.  Set invariance in control , 1999, Autom..

[12]  Derong Liu.  Control Systems With Actuator Saturation: Analysis And Design by T. Hu and Z. Lin; Birkhäuser, Boston, 2001, xvi + 392pp., ISBN 0‐8176‐4219‐6 , 2004 .

[13]  T. Alamo,et al.  Improved computation of ellipsoidal invariant sets for saturated control systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.