A new stability criterion for fixed-point state–space digital filters using two’s complement arithmetic

Shen, Tao; Yuan, Zhugang; Wang, Xiaohong

doi:10.1016/j.automatica.2011.04.008

Cited by 12 publications

(2 citation statements)

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“…It remains a challenge to lessen the conservatism of the existing stability criteria for 2D digital filters involving both quantisation and overflow. Inspired by the works of [29,34,35], an improved method for obtaining the composite non-linearities operating only in quantisation region is developed and a global asymptotic stability criterion for fixed-point 2D digital filters described by FMSLSS model under finite wordlength non-linearities is presented in this paper.…”

Section: Iet Signal Processingmentioning

confidence: 99%

“…Based on the decoupling approximation, the effects of quantisation and overflow have been dealt separately [24–32]. Many researchers have investigated overflow effects in digital filters without considering quantisation [24–29, 34, 35], while others have studied quantisation effects by ignoring overflow [30–32]. However, several researchers have also inquired the certainty of decoupling assumption [36–38].…”

Section: Introductionmentioning

confidence: 99%

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Criterion for non‐existence of limit cycles in 2D state‐space digital filters described by the Fornasini–Marchesini second model with finite wordlength non‐linearities

Agarwal

Kar

2016

IET signal process.

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This study investigates the problem of global asymptotic stability of fixed-point two-dimensional (2D) digital filters described by the Fornasini-Marchesini second local state-space model with the combined effects of quantisation and overflow non-linearities. Utilising a more precise characterisation of the non-linearities, an improved criterion for the limit cycle-free realisation of 2D digital filters is brought out. The criterion is compared with several previously reported criteria. Nomenclatureset of integer numbers Z + set of non-negative integers I n identity matrix of order n 1 n n × 1 vector with all elements equal to 1 0 null matrix or null vector of appropriate dimension f null set x i ith entry of a vector x J t list of coordinate indices, which we regard as a subset of {1, 2, …, n}; the subscript t refers to the iteration number n t number of indices in J t J c t complement set of J t such that J t < J c t = 1, 2, . . . , n { } ; the superscript c stands for the complementmaximum normalised quantisation error N max maximum representable number for a given wordlength T superscript 'T' refers to the transpose R > 0 R is positive definite symmetric matrix l min (P) minimum eigenvalue of matrix P l max (P) maximum eigenvalue of matrix P . 2 Euclidean norm

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Section: Iet Signal Processingmentioning

confidence: 99%