Predictor-based sampled-data exponential stabilization through continuous-discrete observers

The problem of stabilizing a linear continuous-time system with discrete-time measurements and a sampled input with a pointwise constant delay is considered. In a first part, we design a continuous-discrete observer which converges when the maximum time interval between two consecutive measurements is sufficiently small. In a second part, we construct a dynamic output feedback by using a technique which is strongly reminiscent of the reduction model approach. It stabilizes the system when the maximal time between two consecutive sampling instants is sufficiently small. No limitation on the size of the delay is imposed and an ISS property with respect to additive disturbances is established.

[1]  Hassan Hammouri,et al.  Observer Design for Continuous-Discrete Time State Affine Systems up to Output Injection , 2004, Eur. J. Control.

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

[3]  Miroslav Krstic,et al.  Lyapunov-Krasovskii functionals and application to input delay compensation for linear time-invariant systems , 2012, Autom..

[4]  Dorothée Normand-Cyrot,et al.  Reduction Model Approach for Linear Systems With Sampled Delayed Inputs , 2013, IEEE Transactions on Automatic Control.

[5]  Wu-Hua Chen,et al.  Impulsive observer-based stabilisation of uncertain linear systems , 2014 .

[6]  Michael Malisoff,et al.  Reduction Model Approach for Linear Time-Varying Systems With Delays , 2014, IEEE Transactions on Automatic Control.

[7]  Emilia Fridman,et al.  Introduction to Time-Delay Systems: Analysis and Control , 2014 .

[8]  Emilia Fridman,et al.  Predictor-based sampled-data stabilization via continuous-discrete observers , 2014, 53rd IEEE Conference on Decision and Control.

[9]  Emilia Fridman,et al.  A refined input delay approach to sampled-data control , 2010, Autom..

[10]  Yang Tian,et al.  Piecewise-continuous observers for linear systems with sampled and delayed output , 2016, Int. J. Syst. Sci..

[11]  Carlos Canudas-de-Wit,et al.  Remote Stabilization Via Communication Networks With a Distributed Control Law , 2007, IEEE Transactions on Automatic Control.

[12]  Eduardo D. Sontag,et al.  The ISS philosophy as a unifying framework for stability-like behavior , 2001 .

[13]  David Q. Mayne.  Control of linear systems with time delay , 1968 .

[14]  Vincent Andrieu,et al.  Observer design for Lipschitz systems with discrete-time measurements , 2010, 49th IEEE Conference on Decision and Control (CDC).

[15]  Z. Artstein.  Linear systems with delayed controls: A reduction , 1982 .

[16]  Alexander G. Parlos,et al.  Control-relevant discretization of nonlinear systems with time-delay using Taylor-Lie series , 2003, Proceedings of the 2003 American Control Conference, 2003..

[17]  T. Divoux,et al.  Networked control using GPS synchronization , 2006, 2006 American Control Conference.

[18]  Kun Liu,et al.  Wirtinger's inequality and Lyapunov-based sampled-data stabilization , 2012, Autom..

[19]  A. Vande Wouwer,et al.  Improving continuous–discrete interval observers with application to microalgae-based bioprocesses , 2009 .

[20]  Michael Malisoff,et al.  Local Stabilization of Nonlinear Systems Through the Reduction Model Approach , 2014, IEEE Transactions on Automatic Control.

[21]  Iasson Karafyllis,et al.  Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold , 2012, IEEE Transactions on Automatic Control.

[22]  Eduardo Sontag,et al.  Input‐to‐state stability with respect to inputs and their derivatives , 2003 .

[23]  Iasson Karafyllis,et al.  Stabilization of nonlinear delay systems using approximate predictors and high-gain observers , 2013, Autom..

[24]  Wim Michiels,et al.  Finite spectrum assignment of unstable time-delay systems with a safe implementation , 2003, IEEE Trans. Autom. Control..

[25]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[26]  Stefano Di Gennaro,et al.  Stability analisys for a class of sampled nonlinear systems with time-delay , 2010, 49th IEEE Conference on Decision and Control (CDC).

[27]  Hassan Hammouri,et al.  Constant gain observer for continuous-discrete time uniformly observable systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[28]  Rogelio Lozano,et al.  Robustness of a discrete-time predictor-based controller for time-varying measurement delay , 2010 .

[29]  B. Targui,et al.  NONLINEAR CONTINUOUS-DISCRETE OBSERVER APPLICATION TO DISTILLATION COLUMNS , 2011 .

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