Linearisation via input–output injection of time delay systems

ABSTRACT This paper deals with the problem of linearisation of systems with constant commensurable delays by input–output injection using algebraic control tools based on the theory of non-commutative rings. Solutions for the problem of linearisation free of delays, and with delays of an observable nonlinear time-delay systems are presented based on the analysis of the input–output equation. These results are achieved by means of constructive algorithms that use the nth derivative of the output expressed in terms of the state-space variables instead of the explicit computation of the input–output representation of the system. Necessary and sufficient conditions are established in both cases by means of an invertible change of coordinates.

[1]  Xiaohua Xia,et al.  Analysis of nonlinear time-delay systems using modules over non-commutative rings , 2002, Autom..

[2]  Claude H. Moog,et al.  Extended Lie Brackets for Nonlinear Time-Delay Systems , 2011, IEEE Transactions on Automatic Control.

[3]  Miroslav Halás,et al.  When retarded nonlinear time-delay systems admit an input-output representation of neutral type , 2013, Autom..

[4]  Vincent Andrieu,et al.  On the Existence of a Kazantzis--Kravaris/Luenberger Observer , 2006, SIAM J. Control. Optim..

[5]  Driss Boutat,et al.  Finite time observation of nonlinear time-delay systems with unknown inputs , 2010 .

[6]  Driss Boutat,et al.  On Observation of Time-Delay Systems With Unknown Inputs , 2011, IEEE Transactions on Automatic Control.

[7]  Driss Boutat,et al.  Causal observability of nonlinear time-delay systems with unknown inputs , 2010, 49th IEEE Conference on Decision and Control (CDC).

[8]  Claude H. Moog,et al.  Linearization of time-delay systems by input-output injection and output transformation , 2013, Autom..

[9]  T. Erneux.  Applied Delay Differential Equations , 2009 .

[10]  Horst R. Thieme,et al.  Persistence of bacteria and phages in a chemostat , 2012, Journal of mathematical biology.

[11]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[12]  Xiaofan Yang,et al.  The spread of computer viruses under the influence of removable storage devices , 2012, Appl. Math. Comput..

[13]  Martín Velasco-Villa,et al.  Observability and observers for nonlinear systems with time delays , 2000, Kybernetika.