Exact stability analysis of 2D systems using LMIs

In this paper, we propose necessary and sufficient conditions for asymptotic stability analysis of 2D systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions to verify the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that we can reduce the size of LMIs by employing the generalized S-procedure.