Abstract
During the past few decades, two and higher dimensional systems have been extensively applied in many areas of research. The representation of the 2-D systems in the frequency domain is usually given by its transfer function. The bounded-input bounded-output (BIBO) stability of the two dimensional discrete systems depends on the zeros of the characteristic polynomial which is the denominator of this transfer function. In this paper, a new sufficient criterion for the stability of two-dimensional linear shift-invariant discrete systems is presented. The new criterion is based on the sufficient condition for stable polynomials with complex coefficients and the stability criterion for 2-D discrete systems proposed by Murray and Delsarte et al. . The new criterion is non-conservative for the stability testing of 2-D discrete systems. It is shown that the proposed sufficient criterion is simple enough to be applied for the stability checking of the 2-D discrete systems. The utility of the proposed criterion is demonstrated by examples.
Highlights
D URING the past few decades, two and higher dimensional systems have been extensively applied in many areas of the study of broadband beamforming, digital filtering, image processing, multipass processes, gas filtration, thermal processes, geophysics, medical electronics, video and lightfield processing, sensor networks, 2-D discrete control systems, and so on [1] - [11]
The stability analysis of 2-D discrete systems was studied in the frequency domain leading to many well known criteria and tests [12], [13] - [29]
By using the sufficient conditions in [30], [31], the stability checking of the 2-D discrete systems can be carried out rapidly
Summary
D URING the past few decades, two and higher dimensional systems have been extensively applied in many areas of the study of broadband beamforming, digital filtering, image processing, multipass processes, gas filtration, thermal processes, geophysics, medical electronics, video and lightfield processing, sensor networks, 2-D discrete control systems, and so on [1] - [11]. INDEX TERMS 2-D Discrete systems, Transfer function, Polynomials, Stability, Sufficient condition Criteria which provide sufficient and necessary conditions for the stability of 2-D discrete systems have been developed. Such contributions for the stability of 2-D discrete systems have been presented in [30], [31]. By using the sufficient conditions in [30], [31], the stability checking of the 2-D discrete systems can be carried out rapidly.
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