Strong stabilisation by output feedback controller for linear systems with delayed input

This study addresses the strong stabilisation problem for continuous-time linear systems with an unknown input delay via dynamic output feedback controllers. A new criterion for dynamic output feedback stabilisability is proposed in terms of matrix inequalities with the separation of the controller gain with the Lyapunov matrix and the system matrices. Based on these new characterisations, an iterative algorithm is given to design the dynamic output feedback controllers with the initial values obtained by some proposed state feedback stabilisation methods. The effectiveness and merits of the proposed approach are shown through several examples.