An LMI approach to design extended predictor feedback controllers for dynamical systems with input delay

The stabilisation of dynamical systems with input delay by an extended predictor feedback controller is investigated. After considering a more general case of the predictor feedback controllers, the design procedure is transformed into the stabilisation problem of the system controlled by a dynamic output feedback controller. By proposing appropriate Lyapunov-Krasovskii functionals, the predictor feedback gains are then synthesised from the stability conditions which are obtained in form of linear matrix inequalities. Such design approach is more flexible and extendable in comparison to one used by the conventional predictor feedback control. As a simulation example, the designed extended predictor feedback controller is applied on an active suspension system and is used to stabilise an unstable system with input delays. The obtained results demonstrate the effectiveness of the design method.