Passive IIR deconvolution of two-dimensional digital systems subject to missing measurements

This paper deals with the deconvolution problem for two-dimensional (2-D) digital systems which are expressed by the Fornasini–Marchesini local state-space model. Since the sensor measurements are not ideal in many applications, the phenomenon of missing measurements is considered for the deconvolution. A 2-D infinite impulse response (IIR) deconvolution filter is proposed to reconstruct the original signal transmitted through the 2-D digital channel. The phenomenon of missing measurements is described by a Bernoulli process. As a stochastic variable is involved in the deconvolution filtering error system, the mean-square stability is investigated. Beside the stability, to investigate the performance of deconvolution filtering on attenuating the disturbance, the passivity and the dissipation are both studied. With the obtained results, the filter design approach is proposed and the filter gains can be obtained by solving a condition in the expression of linear matrix inequality. The performance of designed filter is demonstrated with a numerical example.