Improved Discretization Method for Uncertain Linear Systems: A Descriptor System Based Approach

This paper investigates an alternative approach for the discretization of uncertain time-invariant continuous-time linear systems which allows to employ higher sampling times. The approach consists in creating an artificial discrete-time descriptor system whose discretization error behaves similarly to the one obtained with double the sampling rate of the original system. The resulting discrete-time descriptor model is compounded of homogeneous polynomially parameter-dependent matrices and additive norm bounded terms related to the discretization residual error. A new linear matrix inequality condition is proposed for the synthesis of a robust digital state feedback control law that certifies the closed-loop stability of the hybrid system. Numerical examples are presented to illustrate how larger sampling times can be used in the proposed method when compared to other works in the literature.