Hybrid output feedback stabilization of two-dimensional linear control systems

We solve for two-dimensional SISO linear control systems the open problem whether there exists finite-state hybrid output feedback to stabilize the systems. We show that under reasonable assumptions, such as stabilizability and detectability conditions, the answer to this question is affirmative for the case of 2-state output feedback. We also address a simulation procedure to locate the stabilizable regions for switched systems consisting of two subsystems. We demonstrate the applicability of our results by considering several specific examples.

[1]  W. Wolovich.  Linear multivariable systems , 1974 .

[2]  M. Branicky.  Stability of switched and hybrid systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  Zvi Artstein,et al.  Examples of Stabilization with Hybrid Feedback , 1996, Hybrid Systems.

[4]  S. Pettersson,et al.  Stability and robustness for hybrid systems , 1996, Proceedings of 35th IEEE Conference on Decision and Control.

[5]  Chaouki T. Abdallah,et al.  Static output feedback: a survey , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[6]  R. Decarlo,et al.  Solution of coupled Lyapunov equations for the stabilization of multimodal linear systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[7]  Daniel Liberzon,et al.  Stabilizing a Linear System With Finite-State Hybrid Output Feedback , 1998 .

[8]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[9]  A. Michel,et al.  Robust stabilizing control laws for a class of second-order switched systems , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[10]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[11]  A. N. Michel,et al.  Stability analysis of digital feedback control systems with time-varying sampling periods , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[12]  Panos J. Antsaklis,et al.  Design of stabilizing control laws for second-order switched systems , 1999 .

[13]  Elena Litsyn,et al.  Stabilization of Linear Differential Systems via Hybrid Feedback Controls , 2000, SIAM J. Control. Optim..

[14]  Xuping Xu,et al.  Stabilization of second-order LTI switched systems , 2000 .