Exact characterization of invariant ellipsoids for linear systems with saturating actuators

We present a necessary and sufficient condition for an ellipsoid to be an invariant set of a linear system under a saturated linear feedback. The condition is given in terms of linear matrix inequalities and can be easily used for optimization based analysis and design.

[1]  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).

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

[3]  Zongli Lin,et al.  On enlarging the basin of attraction for linear systems under saturated linear feedback , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[4]  S. Weissenberger,et al.  Application of results from the absolute stability problem to the computation of finite stability domains , 1968 .

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

[6]  Sophie Tarbouriech,et al.  Output feedback robust stabilization of uncertain linear systems with saturating controls , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[7]  Tingshu Hu,et al.  On enlarging the basin of attraction for linear systems under saturated linear feedback , 2000 .

[8]  P. R. Bélanger,et al.  Piecewise-linear LQ control for systems with input constraints , 1994, Autom..

[9]  Tingshu Hu,et al.  On maximizing the convergence rate for linear systems with input saturation , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[10]  Tingshu Hu,et al.  On maximizing the convergence rate for linear systems with input saturation , 2003, IEEE Trans. Autom. Control..

[11]  K. T. Tan,et al.  Linear systems with state and control constraints: the theory and application of maximal output admissible sets , 1991 .

[12]  E. Davison,et al.  A computational method for determining quadratic lyapunov functions for non-linear systems , 1971 .

[13]  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).