Stabilizing a nonlinear system with limited information feedback

This paper is concerned with the problem of stabilizing a nonlinear continuous-time system by using sampled encoded measurements of the state. We demonstrate that global asymptotic stabilization is possible if a suitable relationship holds between the number of values taken by the encoder, the sampling period, and a system parameter, provided that a feedback law achieving input-to-state stability with respect to measurement errors can be found.

[1]  Wing Shing Wong,et al.  Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback , 1999, IEEE Trans. Autom. Control..

[2]  R. Freeman,et al.  Robust Nonlinear Control Design: State-Space and Lyapunov Techniques , 1996 .

[3]  Zhong-Ping Jiang,et al.  Robust control of uncertain nonlinear systems via measurement feedback , 1999, IEEE Trans. Autom. Control..

[4]  I. Petersen,et al.  Multi-rate stabilization of multivariable discrete-time linear systems via a limited capacity communication channel , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[5]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[6]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[7]  Eduardo Sontag,et al.  On characterizations of the input-to-state stability property , 1995 .

[8]  Randy A. Freeman,et al.  Robust Nonlinear Control Design , 1996 .

[9]  Nicolas Chung Siong Fah,et al.  Input-to-state stability with respect to measurement disturbances for one-dimensional systems , 1999 .

[10]  John Baillieul,et al.  Feedback Designs in Information-Based Control , 2002 .

[11]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[12]  J. Hespanha,et al.  Towards the Control of Linear Systems with Minimum Bit-Rate , 2002 .

[13]  Alberto Isidori,et al.  Stabilizability by state feedback implies stabilizability by encoded state feedback , 2004, Syst. Control. Lett..

[14]  David Angeli,et al.  A Unifying Integral ISS Framework for Stability of Nonlinear Cascades , 2001, SIAM J. Control. Optim..

[15]  R. Freeman.  Global internal stabilizability does not imply global external stabilizability for small sensor disturbances , 1995, IEEE Trans. Autom. Control..

[16]  Daniel Liberzon,et al.  On stabilization of linear systems with limited information , 2003, IEEE Trans. Autom. Control..

[17]  C. De Persis,et al.  A note on stabilization via communication channel in the presence of input constraints , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[18]  C. D. Persis.  n-Bit stabilization of n-Dimensional nonlinear systems in feedforward form , 2004 .

[19]  Claudio De Persis,et al.  n-bit stabilization of n-dimensional nonlinear systems in feedforward form , 2004, IEEE Transactions on Automatic Control.