Admissibility analysis of multidimensional singular systems

The effectiveness of this work lies in the admissibility problem of multidimensional singular linear dD systems described by Roesser models (continuous, discrete and continuous-discrete-time) (for d⩾2). Sufficient conditions for regularity, non-impulsivity and stability of multidimensional linear dD singular systems are proposed in terms of linear matrix inequalities (LMI) for considered models. Sufficient conditions for the existence of a state feedback controller such that the obtained closed-loop dD systems are admissible are then established. To demonstrate the usefulness and effectiveness of our results, we provide practical numerical example of a spatially interconnected electric circuit which is described by a 3 D singular Roesser model to show the applicability and accuracy of the proposed approach.