On semi-global stabilizability of anti-stable systems by saturated linear feedback

It was recently established that a second-order anti-stable linear system can be semi-globally stabilized on its null controllable region by saturated linear feedback and a higher order linear system with two or more anti-stable poles can be semi-globally stabilized on its null controllable region by more general bounded feedback laws. We will show in this paper that a system with three real-valued anti-stable poles cannot be semi-globally stabilized on its null controllable region by the simple saturated linear feedback.

[1]  Tingshu Hu,et al.  Semi-global stabilization with guaranteed regional performance of linear systems subject to actuator saturation , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[2]  R. Suárez,et al.  Linear systems with bounded inputs : global stabilization with eigenvalue placement , 1997 .

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

[4]  Tingshu Hu,et al.  Stabilization of exponentially unstable linear systems with saturating actuators , 2001, IEEE Trans. Autom. Control..

[5]  A. Megretski,et al.  L 2 Bibo Output Feedback Stabilization With Saturated Control , 1996 .

[6]  Zongli Lin,et al.  Semi-global Exponential Stabilization of Linear Systems Subject to \input Saturation" via Linear Feedbacks , 1993 .

[7]  A. Teel.  Linear systems with input nonlinearities: Global stabilization by scheduling a family of H∞-type controllers , 1995 .

[8]  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 .

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

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

[11]  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.

[12]  A. Fuller.  In-the-large stability of relay and saturating control systems with linear controllers , 1969 .

[13]  A. Teel.  Global stabilization and restricted tracking for multiple integrators with bounded controls , 1992 .

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