In this paper we present and discuss a new class of singular fractional systems in a multidimensional state space described by the Roesser continuous-time models. The necessary and sufficient conditions for the asymptotic stability and admissibility by the use of linear matrix inequalities are established. All the obtained results are simulated by some numerical examples to show the applicability and accuracy of our approach.

The main objective of this work is to provide a closed formula for the backward and symmetric solution of the 2-D implicit Roesser model. The relative forward and backward fundamental matrix is of fundamental importance in our approach. An algorithm for the

determination of the backward fundamental matrix sequense is also given.