Output feedback stabilizability and stabilization algorithms for 2D systems

Xu, Li; Saito, Osami; Abe, Kenichi

doi:10.1007/bf00985862

Cited by 42 publications

(30 citation statements)

References 23 publications

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“…For example, the stability of 2D systems based on Lyapunov approaches was investigated in [1,2]; the 2D dynamic output feedback control that is based on solving a set of 2D polynomial equation was investigated in [3]; and the model approximation problem for 2D systems was addressed in [4]. With the development of linear matrix inequality approaches, the works have been extended to systems with parameter uncertainties.…”

Section: Introductionmentioning

confidence: 99%

Robust H ∞ filter design for 2D discrete systems in Roesser model

Gao

Duan

Meng

2008

Int. J. Autom. Comput.

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This paper investigates the robust H∞ filtering problem for uncertain two-dimensional (2D) systems described by the Roesser model. The parameter uncertainties considered in this paper are assumed to be of polytopic type. A new structured polynomially parameter-dependent method is utilized, which is based on homogeneous polynomially parameter-dependent matrices of arbitrary degree. The proposed method includes results in the quadratic framework and the linearly parameter-dependent framework as special cases for zeroth degree and first degree, respectively. A numerical example illustrates the feasibility and advantage of the proposed filter design methods.

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Section: Introductionmentioning

confidence: 99%

Robust H ∞ filter design for 2D discrete systems in Roesser model

Gao

Duan

Meng

2008

Int. J. Autom. Comput.

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“…There are several methods for solving (7) (see [11,15,17]). As Gröbner basis algorithm is constructive and efficient, we review here two methods that use Gröbner bases to solve (7) in the design of synthesis nD FIR, PR filter banks.…”

Section: Synthesis Filters In Nd Fir Pr Filter Banksmentioning

confidence: 99%

“…It was shown in [8], [17] that Gröbner bases were an attractive and efficient method. In the 2D case, for factor coprime rational functionsfi(z1, z2)'s, the variety of the ideal generated byfi(z1, z2)'s is of zero-dimension, and the desirable 2D stable polynomial s(z1, z2) can be easily constructed.…”

Section: Multidimensional Iir Filter Banksmentioning

confidence: 99%

“…In the 2D case, for factor coprime rational functionsfi(z1, z2)'s, the variety of the ideal generated byfi(z1, z2)'s is of zero-dimension, and the desirable 2D stable polynomial s(z1, z2) can be easily constructed. The results on solving equation (9) originally for the 2D control problem [8], [17] were successfully explored in [7] for the design of causal, stable, PR, 2D IIR filter banks. However, its generalization to the nD (n > 2) case is still unresolved.…”

Section: Multidimensional Iir Filter Banksmentioning

confidence: 99%

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Design of multidimensional filter banks using Grobner bases: a survey

Lin

Xu²,

Wu³

2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512)

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This paper surveys on the design of multidimensional filter banks using Gröbner bases. As multidimensional filter banks can be represented by multivariate rational matrices, Gröbner bases are a very effective tool in dealing with multidimensional filter banks. While there are several methods for designing multidimensional FIR filter banks using Gröbner bases, fewer results are available for the IIR counterpart. After reviewing the existing results in the design of multidimensional filter banks using Gröbner bases, we point out the feasibility of designing two classes of causal, stable, perfect reconstruction multidimensional IIR filter banks by exploiting results in multidimensional feedback control system design.

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“…It was shown in [10], [20] that Grobner bases were the attractive and efficient method. In the 2D case, for factor coprime rational func_tions ft(zl,z2)'s, the variety of the ideal generated by j;(zl, ~2 ) ' s is of zero-dimension, and the desirable 2D stable polynomial S ( Z~, Z Z ) can be easily constructed.…”

Section: Let F ( R ) E R[r] F(z) Is Said To Be a Stable Polynomial Imentioning

confidence: 99%

Grobner bases and applications in the design of multidimensional iir filter banks

Lin

Xu²,

Wu³

Fourth International Conference on Information, Communications and Signal Processing, 2003 and the Fourth Pacific Rim Conferenc

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In this paper, we first give a tutorial on the Grobner bases method. Then it is shown that existing results in multidimensional (nD) feedback control theory using Grobner bases can be applied to the design of two classes of nD causal, stable, perfect reconstruction IIR filter banks. We give an elementary treatment on Grobner bases here, in the hope that it will further bring awareness of and stimulate interest in Grobner bases among researchers in signal and image processing in general, and in the design of nD IIR filter banks in particular.

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Output feedback stabilizability and stabilization algorithms for 2D systems

Cited by 42 publications

References 23 publications

Robust H ∞ filter design for 2D discrete systems in Roesser model

Robust H ∞ filter design for 2D discrete systems in Roesser model

Design of multidimensional filter banks using Grobner bases: a survey

Grobner bases and applications in the design of multidimensional iir filter banks

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