Hankel norm performance of 2-D digital filters described by Roesser model with overflow arithmetic

ABSTRACT This paper is concerned with the problem of asymptotic stability with Hankel norm performance (HNP) of two-dimensional (2-D) digital filter characterised by Roesser model, where the 2-D system includes overflow nonlinearities and external interference or excitation of finite duration. The underlying nonlinearities cover the usual types of overflow arithmetic utilised in practice such as saturation, two’s complement, zeroing and triangular. To solve this problem, new sufficient criterion is proposed by employing quadratic 2-D Lyapunov function. The proposed criterion guarantees that the addressed system has 2-D HNP bound. This criterion can examine the unwanted memory effect (ME) reduction of 2-D interfered digital filters for past excitations. In the absence of external inputs, the asymptotic convergence of 2-D digital filters is established under the proposed criterion. The developed HNP criterion is in linear matrix inequality framework and, therefore, computationally tractable. In addition, the optimisation problem is formulated to obtain the minimum HNP of the 2-D interfered digital filter. To illustrate the effectiveness of the proposed criterion, a numerical example is provided. The criteria addressed in current paper can give a whole analysis framework for the unwanted MEs of filters.