On feedback stabilization of nonlinear systems under quantization

The aim of this note is to show how the results in D. Liberzon, "Hybrid feedback stabilization of systems with quantized signals", Automatica, 39, 1543-1554, 2003, concerning asymptotic stabilization using quantized feedback, still hold under the assumption of asymptotic stabilizability only. As a consequence, we are able to examine as special interesting cases nonlinear systems which are e.g. globally asymptotically and locally exponentially stabilizable and stabilizable by dynamic observer-based feedback. The results are also discussed for discrete-time nonlinear systems.

[1]  Sandro Zampieri,et al.  Quantized stabilization of linear systems: complexity versus performance , 2004, IEEE Transactions on Automatic Control.

[2]  Alberto Isidori,et al.  Nonlinear Control Systems II , 1999 .

[3]  F. Mazene,et al.  Global asymptotic output feedback stabilization of feedforward systems , 2001, ECC.

[4]  A. Isidori.  Nonlinear Control Systems , 1985 .

[5]  Daniel Liberzon,et al.  Hybrid feedback stabilization of systems with quantized signals , 2003, Autom..

[6]  Murat Arcak,et al.  A relaxed condition for stability of nonlinear observer-based controllers , 2004, Syst. Control. Lett..

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

[8]  H. Ishii,et al.  Remote control of LTI systems over networks with state quantization , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[9]  N. Elia,et al.  Quantized feedback stabilization of non-linear affine systems , 2004 .

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

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

[12]  A. Bicchi,et al.  SYNTHESIS FOR PRACTICAL STABILIZATION OF QUANTIZED LINEAR SYSTEMS , 2022 .

[13]  John Baillieul,et al.  Data-rate requirements for nonlinear Feedback control , 2004 .

[14]  R. Evans,et al.  Stabilization with data-rate-limited feedback: tightest attainable bounds , 2000 .

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

[16]  Bruce A. Francis,et al.  Stabilizing a linear system by switching control with dwell time , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[17]  F. Fagnani,et al.  Stability analysis and synthesis for scalar linear systems with a quantized feedback , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[18]  John Baillieul,et al.  Robust quantization for digital finite communication bandwidth (DFCB) control , 2004, IEEE Transactions on Automatic Control.

[19]  João Pedro Hespanha,et al.  Stabilization of nonlinear systems with limited information feedback , 2005, IEEE Transactions on Automatic Control.

[20]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[21]  Robin J. Evans,et al.  Topological feedback entropy and Nonlinear stabilization , 2004, IEEE Transactions on Automatic Control.

[22]  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).