Differential flatness of linear non-commensurate time-delay systems with applications to finite spectrum assignment

This paper investigates the differential flatness of linear non-commensurate time-delay systems (TDSs). Based on the coprime factorisation and Bezout identity on multi-polynomial ring, the flat output of linear non-commensurate TDSs can be constructed explicitly. Thus the linear non-commensurate TDSs can be transformed into a high-order fully actuated system (HOFAS) model with its flat output as generalised state. On the basis of HOFAS method, the state feedback controller can be designed to address the finite spectrum assignment (FSA) problem of linear non-commensurate TDSs directly, which provides a new insight into the investigation of the FSA problem. Besides, by utilising the flat output to parameterise the state and input of TDSs, combined with interpolation theory, the state trajectory planning problem can be solved. By designing the two-degree-of-freedom (2DOF) controller, the state trajectory tracking can be also achieved. Numerical example serves to validate the effectiveness of the proposed approach.