Saturated linear quadratic regulation of uncertain linear systems: Stability region estimation and controller design

This paper considers the problems of estimating the stability region (domain of attraction) and controller design for uncertain linear continuous-time systems with input saturation when linear quadratic (LQ) optimal controller is used. By exploiting the structure of the LQ controller and the property of saturation functions, it is established that the estimation of stability region can be obtained by solving linear matrix inequality (LMI) problems. Moreover, an iterative LMI (ILMI) algorithm is presented to design an LQ controller such that the largest estimated stability region can be obtained. Two examples are given to compare our results with existing ones.

[1]  Sophie Tarbouriech,et al.  Output feedback robust stabilization of uncertain linear systems with saturating controls: an LMI approach , 1999, IEEE Trans. Autom. Control..

[2]  Z. Bien,et al.  Robust stability of uncertain linear systems with saturating actuators , 1994, IEEE Trans. Autom. Control..

[3]  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).

[4]  D. Bernstein,et al.  A chronological bibliography on saturating actuators , 1995 .

[5]  Sophie Tarbouriech,et al.  LMI relaxations for robust stability of linear systems with saturating controls , 1999, Autom..

[6]  Randy A. Freeman,et al.  Achieving maximum regions of attraction for unstable linear systems with control constraints , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

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

[8]  Basil Kouvaritakis,et al.  Stability region for a class of open-loop unstable linear systems: Theory and application , 2000, Autom..

[9]  H. Sussmann,et al.  On the stabilizability of multiple integrators by means of bounded feedback controls , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[10]  Jonathan P. How,et al.  Local control design for systems with saturating actuators using the Popov criteria , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[11]  Andrew R. Teel,et al.  Control of linear systems with saturating actuators , 1996 .

[12]  Sophie Tarbouriech,et al.  Stability regions for linear systems with saturating controls , 1999, 1999 European Control Conference (ECC).

[13]  S. Tarbouriech,et al.  Contractive polyhedra for linear continuous-time systems with saturating controls , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[14]  Dennis S. Bernstein,et al.  Dynamic output feedback compensation for systems with input saturation , 1995, Proceedings of 1995 American Control Conference - ACC'95.

[15]  Eduardo Sontag,et al.  A general result on the stabilization of linear systems using bounded controls , 1994, IEEE Trans. Autom. Control..

[16]  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.