Two-dimensional digital filters with sparse coefficients

Lu, Wu-Sheng; Hinamoto, Takao

doi:10.1007/s11045-010-0129-9

Cited by 52 publications

(65 citation statements)

References 10 publications

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“…They showed that the stability of 2-D discrete systems can be guaranteed if there are some matrices satisfying a certain linear matrix inequality (LMIs). The controller and filter design problems have been addressed in Du et al (2000), Gao et al (2004), Liu et al (1998), Liu and Zhang (2003), Lu and Antoniou (1992), Xie et al (2002), Lin et al (2001), Wu et al (2007Wu et al ( , 2008. Gao et al (2004) addressed the controller and filter design problems of controllers and filters for 2-D systems.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Chen

Lam

Gao

et al. 2011

Multidim Syst Sign Process

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This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.

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Section: Introductionmentioning

confidence: 99%

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Chen

Lam

Gao

et al. 2011

Multidim Syst Sign Process

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“…The set S contains the indices of the coefficients that are forced to zero and so are eliminated from the next iterations. The set can grow at each iteration by the hard thresholding step (14). This means that the size of the optimization problem solved shrinks at each iteration, speeding up the running time of the overall algorithm.…”

Section: Design Of Sparse Filtersmentioning

confidence: 99%

“…The two most popular approaches that are used to induce sparsity are: convex relaxation to l 1 minimization [9] and greedy methods [10]. In this sense, previous work for sparse filter design includes the use of the orthogonal matching pursuit algorithm [11], greedy coefficient elimination [12] and linear programming [12], [13], [14]. In this paper we consider a combination of the two approaches to design filters in the minimax sense.…”

Section: Introductionmentioning

confidence: 99%

Iterative reweighted l1 design of sparse FIR filters

Rusu

Dumitrescu

2012

Signal Processing

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Designing sparse 1D and 2D filters has been the object of research in recent years due mainly to the developments in the field of sparse representations. The main goal is to reduce the implementation complexity of a filter while keeping as much of the performance as possible. This paper describes a new method for designing sparse filters in the minimax sense using a mixture of reweighted l 1 minimization and greedy iterations. The combination proves to be quite efficient; after the reweighted l 1 minimization stage is used to introduce zero coefficients in bulk, a small number of greedy iterations serve to eliminate a few extra coefficients. Experimental results and a comparison with the latest methods show that the proposed method performs very well both in the running speed and in the quality of the solutions obtained.

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“…In the past decades, research on two-dimensional (2-D) discrete systems has rapidly increased due to their extensive practical applications in circuits analysis [1], digital image processing [2], signal filtering [3] and thermal power engineering [4], etc. Thus, the study of 2-D systems is an attractive problem and a number of results have been presented in the literature.…”

Section: Introductionmentioning

confidence: 99%

Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

Singh¹,

Tandon²,

Dhawan³

2016

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This paper considers the problem of delay-dependent robust optimal H ∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be normbounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent γ-suboptimal state feedback robust H ∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H ∞ noise attenuation γ over all admissible parameter uncertainties is established.Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H ∞ controller which minimizes the H ∞ noise attenuation γ of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

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Two-dimensional digital filters with sparse coefficients

Cited by 52 publications

References 10 publications

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Iterative reweighted l1 design of sparse FIR filters

Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

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Two-dimensional digital filters with sparse coefficients

Cited by 52 publications

References 10 publications

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

Iterative reweighted l1 design of sparse FIR filters

Delay-Dependent Robust &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;∞&lt;/sub&gt; Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

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Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model