Global Output Feedback Stabilization of a Class of Nonlinear Systems via Linear Sampled-Data Control

In the literature, it has been proved that under a lower-triangular linear growth condition, a class of uncertain nonlinear systems can be globally stabilized by a linear state feedback controller (Tsinias) and later by a linear output feedback controller (Qian and Lin), both in the continuous-time form. This technical note shows that the same continuous-time system under the same assumption can be globally stabilized by a sampled-data output feedback controller whose observer and control law are discrete-time and linear, and hence can be easily implemented by computers.

[1]  Iasson Karafyllis,et al.  Global stability results for systems under sampled-data control , 2007, 2007 European Control Conference (ECC).

[2]  Chunjiang Qian,et al.  A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[3]  Jifeng Zhang,et al.  Output‐feedback control of a class of stochastic nonlinear systems with linearly bounded unmeasurable states , 2008 .

[4]  J. Gauthier,et al.  A simple observer for nonlinear systems applications to bioreactors , 1992 .

[5]  R. Marino,et al.  Dynamic output feedback linearization and global stabilization , 1991 .

[6]  Ali Saberi,et al.  Adaptive stabilization of a class of nonlinear systems using high-gain feedback , 1986, 1986 25th IEEE Conference on Decision and Control.

[7]  Vincent Andrieu,et al.  A unifying point of view on output feedback designs for global asymptotic stabilization , 2009, Autom..

[8]  Dragan Nesic,et al.  Explicit Computation of the Sampling Period in Emulation of Controllers for Nonlinear Sampled-Data Systems , 2009, IEEE Transactions on Automatic Control.

[9]  Wei Lin,et al.  Output feedback control of a class of nonlinear systems: a nonseparation principle paradigm , 2002, IEEE Trans. Autom. Control..

[10]  Hassan K. Khalil,et al.  Output feedback sampled-data control of nonlinear systems using high-gain observers , 2001, IEEE Trans. Autom. Control..

[11]  Hassan K. Khalil,et al.  Multirate Sampled-Data Output Feedback Control With Application to Smart Material Actuated Systems , 2009, IEEE Transactions on Automatic Control.

[12]  H.K. Khalil.  Output feedback sampled-data stabilization of nonlinear systems , 2004, Proceedings of the 2004 American Control Conference.

[13]  Yu. S. Ledyaev,et al.  Asymptotic controllability implies feedback stabilization , 1997, IEEE Trans. Autom. Control..

[14]  Hassan K. Khalil,et al.  High-gain observers in nonlinear feedback control , 2009, 2009 IEEE International Conference on Control and Automation.

[15]  J. Tsinias.  A theorem on global stabilization of nonlinear systems by linear feedback , 1991 .

[16]  MingQing Xiao,et al.  Nonlinear Observer Design in the Siegel Domain , 2002, SIAM J. Control. Optim..

[17]  M. B. Zarrop,et al.  Book Review: Computer Controlled Systems: theory and design (3rd Ed.) , 1998 .

[18]  Hassan K. Khalil,et al.  Performance recovery under output feedback sampled-data stabilization of a class of nonlinear systems , 2004, IEEE Transactions on Automatic Control.

[19]  P. Kokotovic,et al.  Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete-time approximations , 1999 .

[20]  David H. Owens,et al.  Fast Sampling and Stability of Nonlinear Sampled-Data Systems: Part 1. Existence Theorems , 1990 .