Synthesis of controllers for finite-time stabilisation of LTV continuous-time systems using a discrete-time approach

A methodology for the synthesis of state-feedback controllers, guaranteeing the finite-time stability of linear time-varying continuous-time systems, is proposed in this paper. The main approach consists of obtaining a controller for a discretised version of the original system and, by applying a transformation on the obtained controller, computing the desired continuous-time state-feedback gain. The transformation is derived from a condition, also presented in this paper, that relates the finite-time stability of the discretised system, with a predefined sampling rate, to the original continuous-time representation. Such condition, if feasible, also guarantees the desired behaviour of the original system for the given sampling rate. Numerical experiments illustrate the validity of the approach.