Reduction model approach to linear systems with sampled delayed inputs

Solutions to the problem of globally exponentially stabilizing linear systems with an arbitrarily long pointwise delay with sampled feedbacks are presented. The main result of a contribution by the author and D. Normand-Cyrot is recalled. It is compared with other results available in the literature.

[1]  Wook Hyun Kwon,et al.  Feedback stabilization of linear systems with delayed control , 1980 .

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

[3]  M. Krstić.  Delay Compensation for Nonlinear, Adaptive, and PDE Systems , 2009 .

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

[5]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[6]  A. Olbrot,et al.  Finite spectrum assignment problem for systems with delays , 1979 .

[7]  M. Krstic.  Lyapunov Stability of Linear Predictor Feedback for Time-Varying Input Delay , 2010, IEEE Trans. Autom. Control..

[8]  Alexandre Seuret,et al.  Improved stability analysis of networked control systems under asynchronous sampling and input delay , 2010 .

[9]  Jack K. Hale,et al.  Functional differential equations: Basic theory , 1993 .

[10]  Long Wang,et al.  Stabilization of Networked Control Systems with Data Packet Dropout and Transmission Delays: Continuous-Time Case , 2005, Eur. J. Control.

[11]  Michael Malisoff,et al.  Review of Lyapunov Functions , 2009 .

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

[13]  Nikolaos Bekiaris-Liberis,et al.  Stabilization of linear strict-feedback systems with delayed integrators , 2010, ACC 2010.

[14]  M. Malisoff,et al.  Constructions of Strict Lyapunov Functions , 2009 .

[15]  Mrdjan Jankovic,et al.  Compensation of state-dependent state delay for nonlinear systems , 2012, 2012 American Control Conference (ACC).

[16]  Miroslav Krstic,et al.  Lyapunov Stability of Linear Predictor Feedback for Distributed Input Delays , 2011, IEEE Trans. Autom. Control..

[17]  Andrey Polyakov,et al.  Output stabilization of time-varying input delay systems using interval observation technique , 2013, Autom..

[18]  Astrom.  Computer Controlled Systems , 1990 .

[19]  Emilia Fridman,et al.  Robust sampled-data stabilization of linear systems: an input delay approach , 2004, Autom..

[20]  Miroslav Krstic,et al.  Lyapunov stability of linear predictor feedback for distributed input delays , 2010, 49th IEEE Conference on Decision and Control (CDC).

[21]  Alexandre Seuret,et al.  Stability analysis of networked control systems with asynchronous sampling and input delay , 2011, Proceedings of the 2011 American Control Conference.

[22]  A. Olbrot.  Stabilizability, detectability, and spectrum assignment for linear autonomous systems with general time delays , 1978 .

[23]  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.

[24]  Delphine Bresch-Pietri,et al.  Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $ , 2010, IEEE Transactions on Automatic Control.

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

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

[27]  Michael Malisoff,et al.  Stabilization of linear time varying systems with input delays: Application to rapidly time varying systems , 2013, 52nd IEEE Conference on Decision and Control.

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

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

[30]  Miroslav Krstic,et al.  Nonlinear control under delays that depend on delayed states , 2013, Eur. J. Control.

[31]  Miroslav Krstic,et al.  Nonlinear control under input delays that depend on delayed states , 2013, 52nd IEEE Conference on Decision and Control.