Stability of two-dimensional digital filters described by the Fornasini–Marchesini second model with quantisation and overflow

Dey, Anurita; Kokil, Priyanka; Kar, Haranath

doi:10.1049/iet-spr.2011.0265

Cited by 15 publications

(35 citation statements)

References 33 publications

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“…For comparison, simulation results of this system with conventional time-triggered control scheme are also provided here, and we just assume the controller gains are same with (12), then the states. Fig.5-Fig.7 present the corresponding control input and the transmission indication function.…”

Section: Numerical Examplementioning

confidence: 99%

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Event-triggered control of two-dimensional discrete-time systems in Fornasini-Marchesini (FM) second model

Ding

2014

The 26th Chinese Control and Decision Conference (2014 CCDC)

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This paper deals with the event-triggered control for two-dimensional discrete-time systems described in Fornasini-Marchesini (FM) second model. A distance-2 horizontal/vertical related event-triggering state transmission scheme was proposed, which is a non-trivial generalization of counterpart in 1D system case. Based on the 2D type event-triggering scheme, the problem of closed-loop stability with event-triggered control was addressed by deriving the corresponding LMI-based checking conditions. Furthermore, LMI-optimization based methods were presented for controller and event-generator co-design with stabilization and guaranteed cost control problems. Simulation of a numerical example was carried out to show the effectiveness of the results.

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Section: Numerical Examplementioning

confidence: 99%

“…Furthermore, by letting δ = 0.83, one of the feasible controller gain is K = 0.6693 (12) and the corresponding feasible controller gain is…”

Section: Numerical Examplementioning

confidence: 99%

Event-triggered control of two-dimensional discrete-time systems in Fornasini-Marchesini (FM) second model

Ding

2014

The 26th Chinese Control and Decision Conference (2014 CCDC)

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“…Many researchers have studied overflow effects in digital filters without considering quantization [7-9, 32-36, 38, 41, 42, 48] while others have investigated quantization effects by ignoring overflow [29,30,44]. Several papers [23,31,37,47,49,50] deal with the problem of stability of discrete systems under the combined effects of quantization and overflow nonlinearities. model is originally developed in [33].…”

Section: Introductionmentioning

confidence: 99%

New results on saturation overflow stability of 2-D state-space digital filters described by the Fornasini–Marchesini second model

Agarwal

Kar

2016

Signal Processing

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“…Since the operation of a real digital filter takes place under the combined effects of quantisation and overflow non-linearities, the study of the stability behaviour of digital filters in the presence of both types of non-linearities appears to be more realistic. Pertaining to the study of the combined effects of quantisation and overflow on digital filters, very few publications are available in the literature so far [39][40][41][42][43][44][45][46]. A few criteria for establishing the equivalence between the global asymptotic stability of 2D systems with various combinations of quantisation and overflow and that of 2D systems with only quantisation have been reported [39,41].…”

Section: Introductionmentioning

confidence: 99%

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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Stability of two-dimensional digital filters described by the Fornasini–Marchesini second model with quantisation and overflow

Cited by 15 publications

References 33 publications

Event-triggered control of two-dimensional discrete-time systems in Fornasini-Marchesini (FM) second model

Event-triggered control of two-dimensional discrete-time systems in Fornasini-Marchesini (FM) second model

New results on saturation overflow stability of 2-D state-space digital filters described by the Fornasini–Marchesini second model

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

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