Stabilization of Nonlinear Systems via Periodically Intermittent Control

This brief studies the exponential stabilization problem for a class of nonlinear systems by means of periodically intermittent control. An exponential stability criterion given in terms of a set of linear matrix inequalities, together with a simpler sufficient condition determined by three scalar inequalities, is presented. A suboptimal intermittent controller is designed with respect to the general cost function under the assumption that the control period and control width are fixed and known. Numerical simulations are presented to verify the theoretical results.

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

[2]  L. Shilnikov.  CHUA’S CIRCUIT: RIGOROUS RESULTS AND FUTURE PROBLEMS , 1994 .

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

[4]  R. Brockett.  A stabilization problem , 1999 .

[5]  E. Sánchez,et al.  Input-to-state stability (ISS) analysis for dynamic neural networks , 1999 .

[6]  M. Zochowski.  Intermittent dynamical control , 2000 .

[7]  Izumi Masubuchi,et al.  Advanced performance analysis and robust controller synthesis for time-controlled switched systems with uncertain switchings , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[8]  I. Masubuchi,et al.  Dynamic controller synthesis guaranteeing L/sub 2/-gain for time-controlled switched systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[9]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[10]  Masami Saeki,et al.  Model predictive control for linear parameter varying systems using parameter dependent Lyapunov function , 2006, The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04..

[11]  Q. Han,et al.  State feedback controller design of networked control systems , 2004 .

[12]  Tommy W. S. Chow,et al.  Nonlinear dynamical systems control using a new RNN temporal learning strategy , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  Guanrong Chen,et al.  Controlling a unified chaotic system to hyperchaotic , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  Xiaofan Yang,et al.  Switch control for piecewise affine chaotic systems. , 2006, Chaos.

[15]  Luigi Iannelli,et al.  Dithered Sliding-Mode Control for Switched Systems , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[16]  Wook Hyun Kwon,et al.  ${\cal H}_{\infty}$ Finite Memory Controls for Linear Discrete-Time State-Space Models , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.