Stabilization of planar switched systems

This paper considers the problem of stabilization of single-input planar switched systems. We assume the switching law is observable, a formula is presented, which provides a necessary and sufficient condition for the system to be quadratically stabilizable. A set of linear inequalities are given to describe the set of all quadratic Lyapunov functions. The solvability and the control design technique are clearly described in a straightforward computation algorithm.

[1]  Daniel Liberzon,et al.  Benchmark Problems in Stability and Design of Switched Systems , 1999 .

[2]  S. M. Williams,et al.  Adaptive frequency domain control of PWM switched power line conditioner , 1990 .

[3]  A. Morse,et al.  Stability of switched systems: a Lie-algebraic condition ( , 1999 .

[4]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[5]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[6]  Masayoshi Tomizuka,et al.  Learning hybrid force and position control of robot manipulators , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[7]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

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

[9]  Zhendong Sun,et al.  On reachability and stabilization of switched linear systems , 2001, IEEE Trans. Autom. Control..

[10]  Tatsushi Ooba,et al.  Two conditions concerning common quadratic Lyapunov functions for linear systems , 1997, IEEE Trans. Autom. Control..

[11]  K. Narendra,et al.  A sufficient condition for the existence of a common Lyapunov function for two second order linear systems , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[12]  Yasuyuki Funahashi,et al.  Stability robustness for linear state space models—a Lyapunov mapping approach , 1997 .

[13]  F. Xue,et al.  Necessary and sufficient conditions for adaptive stablizability of jump linear systems , 2001, Commun. Inf. Syst..

[14]  Clyde F. Martin,et al.  A Converse Lyapunov Theorem for a Class of Dynamical Systems which Undergo Switching , 1999, IEEE Transactions on Automatic Control.

[15]  H. Sira-Ramírez.  Nonlinear P-I controller design for switchmode DC-to-DC power converters , 1991 .

[16]  Daizhan Cheng,et al.  On quadratic Lyapunov functions , 2003, IEEE Trans. Autom. Control..

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

[18]  Zheng Guo. Li.  Stability of switched systems. , 2001 .