Stability of 2-D digital filters described by the Roesser model using any combination of quantization and overflow nonlinearities

Kokil, Priyanka; Dey, Anurita; Kar, Haranath

doi:10.1016/j.sigpro.2012.05.016

Cited by 19 publications

(12 citation statements)

References 48 publications

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“…Digital 2D Roesser model discussed in [8,12] is considered as

([], \begin{matrix} center \\ array η^{h} (k + 1, l) \\ array η^{v} (k, l + 1) \end{matrix}) = ([], \begin{matrix} center \\ array O_{Q}^{h} (ξ^{h} (k, l)) \\ array O_{Q}^{v} (ξ^{v} (k, l)) \end{matrix}) + ([], \begin{matrix} center \\ array H^{h} d^{h} (k, l) \\ array H^{v} d^{v} (k, l) \end{matrix}),

([], \begin{matrix} center \\ array ξ^{h} (k, l) \\ array ξ^{v} (k, l) \end{matrix}) = ([], \begin{matrix} center \\ array G_{11} & array G_{12} \\ array G_{21} & array G_{22} \end{matrix}) ([], \begin{matrix} center \\ array η^{h} (k, l) \\ array η^{v} (k, l) \end{matrix}),

where both independent variables in 2D systems belong to real field, that is, k , l ∈ ℜ, and satisfy

k = false{0,1, ⋯, m + 1 false}

and

l = false{0,1, ⋯, n + 1 false}

, η h ( k , l ) ∈ ℜ m and η v ( k ...…”

Section: System Descriptionmentioning

confidence: 99%

“…Remark In contrast to the techniques discussed in literature so far [3‐24], the proposed approach focuses on the overflow oscillation‐free region realization for 2D discrete‐time systems (as expressed in ()), in addition to the stability analysis, as a novel idea to the best of authors' knowledge. Whereas, in the context of establishing overflow oscillation‐free regions, the work in [28] is limited to only 1D systems.…”

Section: Stability Investigationmentioning

confidence: 99%

“…It may be noted that, although, such bounded region has earlier been investigated in [28] but the work is restricted to 1D systems only. The investigation of stability for 2D system is inherently complex and the involvement of multiple parameters makes it more complicated. Furthermore, as opposed to existing methods [12,17], which focus on some specific quantization type, the proposed approach considers a generalized quantization while deriving the stability criteria. Only thing that is needed for quantization is the quantization error bounds in horizontal and vertical dimensions. It should also be noted that the proposed results are derived on the basis of several regions, local stability analysis, and Lyapunov redesign for ensuring overflow‐free regions with a complicated examination.…”

Section: Introductionmentioning

confidence: 99%

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Overflow oscillations‐free realization of discrete‐time 2D Roesser models under quantization and overflow constraints

Malik

Tufail

Rehan

et al. 2021

Asian Journal of Control

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This brief proposes novel linear matrix inequalities-based criteria to investigate the asymptotic convergence of states to an overflow oscillations-free ellipsoidal region for a two-dimensional Roesser digital model subjected to quantization and overflow effects of a digital hardware. Existence of a novel region for two-dimensional Rosser systems is shown in the present study, in which overflow oscillations can be completely removed for realization of a system. New realization conditions for Roesser systems in the absence and presence of external interference along with stability and overflow-free regional behavior are investigated by application of regional analysis, convex routines, and Lyapunov redesign. In contrast to existing literature that primarily focus on a specific type of quantitation and global asymptotic stability, the conditions in the presented work are derived by considering the generalized quantization arithmetic and for guaranteeing convergence of states in a convex oscillations-free region (in the steady-state) in both the absence and presence of bounded interference. The localized stable regions can be directly associated with the word-length employed to realize the two-dimensional systems on a digital hardware. Simulation results are also furnished to validate the efficacy of the proposed approach.

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“…Digital 2D Roesser model discussed in [8,12] is considered as

([], \begin{matrix} center \\ array η^{h} (k + 1, l) \\ array η^{v} (k, l + 1) \end{matrix}) = ([], \begin{matrix} center \\ array O_{Q}^{h} (ξ^{h} (k, l)) \\ array O_{Q}^{v} (ξ^{v} (k, l)) \end{matrix}) + ([], \begin{matrix} center \\ array H^{h} d^{h} (k, l) \\ array H^{v} d^{v} (k, l) \end{matrix}),

([], \begin{matrix} center \\ array ξ^{h} (k, l) \\ array ξ^{v} (k, l) \end{matrix}) = ([], \begin{matrix} center \\ array G_{11} & array G_{12} \\ array G_{21} & array G_{22} \end{matrix}) ([], \begin{matrix} center \\ array η^{h} (k, l) \\ array η^{v} (k, l) \end{matrix}),

where both independent variables in 2D systems belong to real field, that is, k , l ∈ ℜ, and satisfy

k = false{0,1, ⋯, m + 1 false}

and

l = false{0,1, ⋯, n + 1 false}

, η h ( k , l ) ∈ ℜ m and η v ( k ...…”

Section: System Descriptionmentioning

confidence: 99%

Section: Stability Investigationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Overflow oscillations‐free realization of discrete‐time 2D Roesser models under quantization and overflow constraints

Malik

Tufail

Rehan

et al. 2021

Asian Journal of Control

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show abstract

“…Existence of such nonlinearities causes instability to the designed system (Butterweck et al, 1988; Claasen et al, 1976; Oppenheim and Schafer, 1975; Schlichtharle, 2000). Therefore, several researchers have studied the stability properties of digital filters with saturation arithmetic (Ahn, 2011, 2013a, b; Bose and Chen, 1991; Kar, 2007, 2010; Kar and Singh, 1998, 2005; Kokil, 2016; Kokil and Shinde, 2015; Kokil et al, 2012a, 2012b, 2016; Liu and Michel, 1992; Singh, 1990).…”

Section: Introductionmentioning

confidence: 99%

New passivity results for the realization of interfered digital filters utilizing saturation overflow nonlinearities

Parthipan

Arockiaraj

Kokil

2018

Transactions of the Institute of Measurement and Control

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This paper considers the passivity performance analysis of fixed-point state-space digital filters with saturation nonlinearities in the presence of external interference. The purpose is to establish new stability criteria in terms of linear matrix inequality (LMI) such that fixed-point state-space digital filters with saturation nonlinearities in the existence of external interference ensure passivity performance with its storage function. The presented results not only ensure state strict and input state strict passivity in the presence of external interference but also confirm asymptotic stability without external interference. The obtained conditions for fixed-point state-space digital filters are based on passivity properties and, hence, are quite novel to previously proposed criteria. Finally, simulation results are given to demonstrate the effectiveness of the proposed work.

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“…Furthermore, the so-called 2D modeling theory could be applied as an efficient analysis tool to deal with other problems; for example, elimination of overflow oscillations in 2D digital filters employing saturation arithmetic has been implemented be means of LMIs in [6], LMI-based stability analysis of 2D discrete systems described by the Fornasini-Marchesini (FM) second model with state saturation has been addressed in [7], ∞ filter design for 2D Markovian jump systems has been given in [8], and optimal guaranteed cost control of 2D discrete uncertain systems has been studied in [9], respectively. More recently, considering the fact that state saturation often appears in various 2D digital systems when its transfer function is implemented by a state-space model with the finite wordlength format, the problem of stability analysis of 2D state-space digital filters with saturation arithmetic has been deeply investigated in the literature [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] and less conservative LMI-based stability criteria have been persistently obtained. However, it is worth noting that most of the above results are only for certain 2D systems.…”

Section: Introductionmentioning

confidence: 99%

Control Synthesis of Uncertain Roesser‐Type Discrete‐Time Two‐Dimensional Systems

Zhang

Zhao

Wang

et al. 2014

Mathematical Problems in Engineering

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This paper is concerned with control synthesis of uncertain Roesser-type discrete-time two-dimensional (2D) systems. The mathematical model of the 2D system’s parameter uncertainty, which may appear typically in many actual environment, is modeled as a convex bounded uncertain domain. By using the Lyapunov stability theory, stabilization conditions is proposed in with the purpose of ensuring the robust asymptotical stability of the underlying closed-loop uncertain Roesser-type discrete-time 2D systems. Furthermore, the obtained result of this paper is formulated in the form of linear matrix inequalities (LMIs), which can be easily solved via standard numerical software. Finally, a numerical example is also provided to demonstrate the effectiveness of the proposed result.

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Stability of 2-D digital filters described by the Roesser model using any combination of quantization and overflow nonlinearities

Cited by 19 publications

References 48 publications

Overflow oscillations‐free realization of discrete‐time 2D Roesser models under quantization and overflow constraints

Overflow oscillations‐free realization of discrete‐time 2D Roesser models under quantization and overflow constraints

New passivity results for the realization of interfered digital filters utilizing saturation overflow nonlinearities

Control Synthesis of Uncertain Roesser‐Type Discrete‐Time Two‐Dimensional Systems

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