Asynchronous Deconvolution Filtering for 2-D Markov Jump Systems With Packet Loss Compensation

In this work, we address the issue of asynchronous deconvolution filter design for 2-D Markov jump systems with random packet losses. First, the considered plant is established by a well-known Fornasini-Marchesini model. Then, an asynchronous 2-D deconvolution filter is proposed to reconstruct the 2-D signal with measurement noise to satisfy a prescribed performance specification. The asynchronization phenomenon between the system modes and filter modes is characterized by a hidden Markov model. Besides, in practical applications, the congestion of the transmission channel between the system and the filter may lead to data losses, which may make the system performance degraded or even unstable. For this, an improved 2-D single exponential smoothing scheme is proposed to generate some predictions of the lost information to compensate for lost packets. By means of the 2-D Lyapunov stability theory, some sufficient conditions are acquired, which can make the resultant system asymptotic mean-square stable and satisfies an $\mathcal {H}_{\infty }$ disturbance attenuation performance. At last, an example concerning image processing is adopted to verify the correctness of the presented asynchronous 2-D deconvolution filtering scheme. Note to Practitioners—In practical applications, many dynamics may suffer from undergoing sudden structural or parameter changes, resulting in a system that is difficult to describe clearly. The Markov jump systems, consisting of states and modes, can handle this problem satisfactorily. Considering the effects of some unfavorable factors, i.e., delay, quantization, and environmental noise, a hidden Markov model is employed to handle the asynchronous problem between the system and the filter. On the other hand, the emergence of 2-D systems effectively solves the problem of the system’s state evolving in two directions. In addition, the congestion of the transmission channel between the system and the filter may lead to data loss. To compensate for the impact of data packet loss, an improved 2-D single exponential smoothing scheme is proposed.

I. Introduction

Markov jump systems (MJSs), consisting of a class of subsystems, have sparked a reiterative research interest over the past few decades. The transitions among these subsystems are managed through a set of Markov chains. In virtue of the specific architecture, MJSs are widely employed to describe some complex systems whose dynamic behavior may undergo sudden structural or parameter changes [1], [2], [3], [4], [5]. Currently, the investigation of MJSs has achieved abundant developments. By relaxing constant transfer rates of general MJSs to be time-varying, a robust stochastic stability condition and a robust controller for semi-MJSs were presented in [6]. Further, in the case that the internet delay or packet losses were variable in distinct working regions, the investigation in [7] raised a filtering scheme for non-homogeneous MJSs. Assuming that the transition probabilities cannot be fully acquired, the prominent improvement of [8] was to design a fault detection filter for MJSs with partially accessible transition probabilities.