LMI-based stability condition for 2D discrete systems described by the Fornasini-Marchesini second model

This paper presents a stability criterion for 2D discrete systems described by the Fornasini-Marchesini second model. The method presented in this paper is based on linear matrix inequalities (LMI), and hence, it is computationally tractable. In deriving the method, finite-order Fourier series approximation of the solution for frequency-dependent LMI (FDLMI), and the properties of quadratic form representation of finite-order Fourier series play key roles. From the view point of the proposed method, the existing LMI-based condition can be regarded as the one which is obtained by Fourier series approximation of order zero, and thus, it is expected that the proposed method leads to less conservative results. This is illustrated by a numerical example.