Stability analysis and H∞ norm computation of 2-D discrete systems using linear matrix inequalities

This paper presents a stability criterion and a method for computing the H_∞ norm of 2-D discrete systems. Both methods are based on linear matrix inequalities (LMI), and hence, they are computationally tractable. In deriving these methods, 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 methods, the existing LMI-based methods can be regarded as the ones which are obtained by Fourier series approximation of order zero, and thus, it is expected that the proposed methods lead to less conservative results. This is illustrated by numerical examples.