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Robust Stabilization for Standard Discrete-Time Fuzzy Singularly Perturbed Systems: A spectral norm Approach

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Robust Stabilization for Standard Discrete-Time Fuzzy Singul...

THE EIGENVALUE PERTURBATION BOUND FOR ARBITRARY MATRICES

第25届中国控制与决策会议

作者： Liye Yu Jinxiang Chen State Key Laboratory of Hybrid Process Industry Automation System and Equipment Technology Automation Research and Design Institute of Metallurgical Industry China Iron ＆ Steel Research Institute Group

ISBN: (纸本)9781467355322

This paper presents a new approach for stabilizing standard discrete-time fuzzy singularly perturbed systems（SPSs） via a state feedback controller. Without using conventional Lyapunov function, based on the matrix spectral norm of the closed-loop system, a new ε-independent sufficient condition is presented. In contrast to the existing results, the proposed method can improve the upper bounds of singular perturbation parameter ε. Two examples are provided to illustrate the reduced conservatism of our results.

关键词： Singularly perturbed systems discrete-time systems nonlinear systems linear matrix inequalities(LMIs) spectral norm robust control.

来源： cnki会议评论

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Journal of Computational Mathematics 2006年第2期24卷 141-148页

作者： Wen Li Jian-xin Chen School of Mathematical Sciences South China Normal University Guangzhou 510631 China College of Applied Mathematics Guangdong University of Technology Guangzhou 510090 China

In this paper we present some new absolute and relative perturbation bounds for the eigenvalue for arbitrary matrices, which improves some recent results. The eigenvalue inclusion region is also discussed.

关键词： Eigenvalue perturbation bound Jordan canonical form Frobenius norm spectral norm Inclusion region.

Acute perturbation,of Drazin inverse and oblique projectors

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Frontiers of Mathematics in China 2018年第6期13卷 1427-1445页

作者： Sanzheng QIAO Yimin WEI Department of Computing and Software McMaster UniversityHamiltonON L8S 4K1 Canada School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics Fudan UniversityShanghai 200433China

For an n×n complex matrix A with ind(A) = r; let AD and Aπ = I-AAD be respectively the Drazin inverse and the eigenprojection corresponding to the eigenvalue 0 of A: For an n×n complex singular matrix B with ind(B) = s, it is said to be a stable perturbation of A, if I-(Bπ-Aπ)2 is nonsingular, equivalently, if the matrix B satisfies the condition \(\mathcal{R}(B^s)\cap\mathcal{N}(A^r)=\left\{0\right\}\) and \(\mathcal{N}(B^s)\cap\mathcal{R}(A^r)=\left\{0\right\}\), introduced by Castro-González, Robles, and Vélez-Cerrada. In this paper, we call B an acute perturbation of A with respect to the Drazin inverse if the spectral radius ρ(Bπ-Aπ) spectral radius, instead of the usual spectral norm, is used. Our results include the previous results on the Drazin inverse and the group inverse as special cases and are consistent with the previous work on the spectral projections and the Moore-Penrose inverse.

关键词： Drazin inverse acute perturbation stable perturbation spectral radius spectral norm oblique projection

On the norms of r-Hankel Matrices Involving Fibonacci and Lucas Numbers

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Journal of Applied Mathematics and Physics 2018年第7期6卷 1409-1417页

作者： Hasan Gokbas Hasan Kose Semsi Tebrizi Girl Anatolian Religious Vocational High School KonyaTurkey Science Faculty Selcuk UniverstyKonyaTurkey

Let us define A=Hr=(aij)?to be n×n?r-Hankel matrix. The entries of matrix A are Fn=Fi+j-2?or Ln=Fi+j-2?where Fn?and Ln?denote the usual Fibonacci and Lucas numbers, respectively. Then, we obtained upper and lower bounds for the spectral norm of matrix A. We compared our bounds with exact value of matrix A’s spectral norm. These kinds of matrices have connections with signal and image processing, time series analysis and many other problems.

关键词： Euclidean norm spectral norm r-Hankel Matrix Fibonacci Numbers Lucas Numbers

On the norms of r-Toeplitz Matrices Involving Fibonacci and Lucas Numbers

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Advances in Linear Algebra & Matrix Theory 2016年第2期6卷 31-39页

作者： Hasan Gökbaş Ramazan Türkmen Semsi Tebrizi Anatolian Religious Vocational High School Konya Turkey Science Faculty Selcuk University Konya Turkey

Let us define to be a r-Toeplitz matrix. The entries in the first row of are or;where Fn and Ln denote the usual Fibonacci and Lucas numbers, respectively. We obtained some bounds for the spectral norm of these ma... 详细信息

关键词： r-Toeplitz Matrix Fibonacci Numbers Lucas Numbers spectral norm