Pseudo predictor feedback stabilisation of linear systems with both state and input delays

This paper proposes a pseudo predictor feedback control scheme for stabilisation of linear systems with both input and state delays. It is proved that the stability of the closed-loop system is determined by the stability of the target closed-loop system, along with the stability of an associated integral delay system, which describes the additional dynamics induced by the pseudo predictor. It is shown that in case of commensurate delays, the control law can be directly expressed as a function of the original system matrices, widening the applicability of analysis and design tools. For the synthesis of the feedback gains, a numerical procedure is presented to solve the simultaneous stabilization problem of the target system and the associated integral delay system. Numerical experiments are carried out to illustrate the effectiveness of the methodology.