A Tensor Product Model Transformation Approach to the Discretization of Uncertain Linear Systems

Most of the discretization approaches for uncertain linear systems make use of the series representation of the matrix exponential function and truncate the summation after a certain order. This usually leads to discrete- time uncertain polytopic models described by polynomial matrices with multiple indexes, which usually means that the higher the order used in the approximation, the higher the number of linear matrix inequalities (LMI) needed. This work, instead, proposes an approach based on a grid of the possible values for the matrix exponential function and an application of the tensor product model transformation technique to find a suitable polytopic model. Numerical examples are presented to illustrate the advantages and the applicability of the proposed technique.