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.

Keywords:

• Nonlinear systems
• time-delay systems
• linearisation
• algebraic tools
• output injection
• input–output representation

Disclosure statement

No potential conflict of interest was reported by the authors.