Robust stability of dynamic predictor based control laws for input and state delay systems

Abstract The robust stability properties of the dynamic predictor scheme for state and input delay systems are analyzed in the frequency domain. Robust stability bounds are presented for the cases of uncertainty of the matrix parameters, of the state or input delay, and of the combination of both. An example illustrates the results.

[1]  R. Bellman The stability of solutions of linear differential equations , 1943 .

[2]  O. J. M. Smith,et al.  A controller to overcome dead time , 1959 .

[3]  Sabine Mondié,et al.  Delay robustness of closed loop finite assignment for input delay systems , 2001 .

[4]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

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

[6]  V. Kharitonov,et al.  Predictor-based controls: The implementation problem , 2015 .

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

[8]  Tomás Vyhlídal,et al.  Mapping Based Algorithm for Large-Scale Computation of Quasi-Polynomial Zeros , 2009, IEEE Transactions on Automatic Control.

[9]  V. Kharitonov Time-Delay Systems: Lyapunov Functionals and Matrices , 2012 .

[10]  C. D. Souza,et al.  Delay-dependent robust stability and stabilization of uncertain linear delay systems: a linear matrix inequality approach , 1997, IEEE Trans. Autom. Control..

[11]  Dirk Roose,et al.  Limitations of a class of stabilization methods for delay systems , 2001, IEEE Trans. Autom. Control..

[12]  Zongli Lin,et al.  Robust output regulation of linear time‐delay systems: A state predictor approach , 2016 .

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

[14]  V. Van Assche,et al.  Some problems arising in the implementation of distributed-delay control laws , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

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

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

[17]  Emilia Fridman,et al.  Parameter dependent stability and stabilization of uncertain time-delay systems , 2003, IEEE Trans. Autom. Control..

[18]  Nikolaos Bekiaris-Liberis Simultaneous compensation of input and state delays for nonlinear systems , 2014, Syst. Control. Lett..

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

[20]  Sabine Mondié,et al.  Approximation of control laws with distributed delays: a necessary condition for stability , 2001, Kybernetika.

[21]  Delphine Bresch-Pietri,et al.  Prediction-Based Control for Linear Systems with Input- and State- Delay – Robustness to Delay Mismatch , 2014 .

[22]  Vladimir L. Kharitonov,et al.  An extension of the prediction scheme to the case of systems with both input and state delay , 2014, Autom..