Continuous observer design for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements

In this paper, continuous observer is designed for a class of multi-output nonlinear systems with multi-rate sampled and delayed output measurements. The time delay may be larger or less than the sampling intervals. The sampled and delayed measurements are used to update the observer whenever they are available. Sufficient conditions are presented to ensure global exponential stability of the observation errors by constructing a Lyapunov-Krasovskii function. A numerical example is given to illustrate the effectiveness of the proposed methods.

[1]  X. Xia,et al.  Nonlinear observer design by observer error linearization , 1989 .

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

[3]  Dragan Nesic,et al.  On emulated nonlinear reduced-order observers for networked control systems , 2012, Autom..

[4]  H. Shim,et al.  Semi-global observer for multi-output nonlinear systems , 2001 .

[5]  Iasson Karafyllis,et al.  From Continuous-Time Design to Sampled-Data Design of Observers , 2009, IEEE Transactions on Automatic Control.

[6]  J. Rudolph,et al.  A block triangular nonlinear observer normal form , 1994 .

[7]  L. Praly.  Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[8]  Hassan Hammouri,et al.  Observer Design for Uniformly Observable Systems With Sampled Measurements , 2013, IEEE Transactions on Automatic Control.

[9]  Françoise Lamnabhi-Lagarrigue,et al.  High gain observer design for some networked control systems , 2010 .

[10]  Dragan Nesic,et al.  A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models , 2004, IEEE Transactions on Automatic Control.

[11]  Françoise Lamnabhi-Lagarrigue,et al.  High gain observer design for nonlinear systems with time varying delayed measurements , 2011 .

[12]  Iasson Karafyllis,et al.  A system-theoretic framework for a wide class of systems II: Input-to-output stability , 2007 .

[13]  J. Gauthier,et al.  Erratum Observability and Observers for Nonlinear Systems , 1995 .

[14]  Iasson Karafyllis,et al.  Global exponential sampled-data observers for nonlinear systems with delayed measurements , 2012, Syst. Control. Lett..

[15]  Xiaohua Xia,et al.  Continuous observer design for nonlinear systems with sampled and delayed output measurements , 2014 .

[16]  Tarek Ahmed-Ali,et al.  Continuous-Discrete Observer for State Affine Systems With Sampled and Delayed Measurements , 2013, IEEE Transactions on Automatic Control.

[17]  J. Gauthier,et al.  High gain estimation for nonlinear systems , 1992 .

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

[19]  Hassan K. Khalil,et al.  Robustness of high-gain observer-based nonlinear controllers to unmodeled actuators and sensors , 2002, Autom..

[20]  Arthur J. Krener,et al.  Linearization by output injection and nonlinear observers , 1983 .

[21]  D. Bestle,et al.  Canonical form observer design for non-linear time-variable systems , 1983 .

[22]  J. Gauthier,et al.  Exponential observers for nonlinear systems , 1993, IEEE Trans. Autom. Control..

[23]  J. Hedrick,et al.  Observer design for a class of nonlinear systems , 1994 .

[24]  F. Thau.  Observing the state of non-linear dynamic systems† , 1973 .

[25]  Frank Allgöwer,et al.  Observer with sample-and-hold updating for Lipschitz nonlinear systems with nonuniformly sampled measurements , 2008, 2008 American Control Conference.

[26]  Alessandro Astolfi,et al.  High gain observers with updated gain and homogeneous correction terms , 2009, Autom..

[27]  M. Zeitz.  The extended Luenberger observer for nonlinear systems , 1987 .

[28]  Xiaohua Xia,et al.  A high-gain-based global finite-time nonlinear observer , 2011, 2011 9th IEEE International Conference on Control and Automation (ICCA).

[29]  Zhong-Ping Jiang,et al.  Small-gain theorem for a wide class of feedback systems with control applications , 2007, 2007 European Control Conference (ECC).

[30]  L. Praly,et al.  Proof of Theorem 2 in "High-gain observers with updated high-gain and homogeneous correction terms" , 2008 .

[31]  Jean-Pierre Barbot,et al.  Discrete-time approximated linearization of SISO systems under output feedback , 1999, IEEE Trans. Autom. Control..

[32]  I. Haskara.  On sliding mode observers via equivalent control approach , 1998 .

[33]  K. Gu.  An integral inequality in the stability problem of time-delay systems , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[34]  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.

[35]  Yuehua Huang,et al.  Uniformly Observable and Globally Lipschitzian Nonlinear Systems Admit Global Finite-Time Observers , 2009, IEEE Transactions on Automatic Control.

[36]  X. Xia,et al.  Semi-global finite-time observers for nonlinear systems , 2008, Autom..

[37]  Dragan Nesic,et al.  A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation , 2004, Autom..

[38]  D. Mayne,et al.  Moving horizon observers and observer-based control , 1995, IEEE Trans. Autom. Control..

[39]  Dragan Nesic,et al.  Emulation-based stabilization of networked control systems implemented on FlexRay , 2015, Autom..

[40]  I. Karafyllis.  A system-theoretic framework for a wide class of systems I: Applications to numerical analysis , 2007 .