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Stability analysis of fuzzy-model-based control systems: application on regulation of switching DC-DC converter

IET CONTROL theory AND applications 2009年第8期3卷 1093-1106页

作者： Lam, H. K. Tan, S. C. Kings Coll London Div Engn London WC2R 2LS England Hong Kong Polytech Univ Elect & Informat Engn Dept Kowloon Hong Kong Peoples R China

This study presents a non-linear design methodology for fuzzy controllers employed in switching DC-DC converters that operates in large-signal domain. Unlike conventional controller design approach, which addresses only the small-signal system stability, the proposed design methodology tackles the design using a non-linear control viewpoint. The proposed approach uses a Tagaki-Sugeno (T-S) fuzzy model to represent the switching converter. The Lyapunov theory is then adopted to derive the sufficient stability conditions in terms of linear matrix inequalities. These inequalities are then employed for the design of a large-signal stable fuzzy controller. Worth mentioning is that the consideration of the circuit parameter uncertainty and the mismatch of the fuzzy membership functions in the proposed approach, greatly complicate the stability analysis, which leads to a conservative result. To alleviate the conservativeness, a membership-function condition is proposed to guide the design of the membership functions of the fuzzy controller. Furthermore, free matrices can be introduced to further relax the conservativeness of stability analysis result. Simulation results on the regulation of a boost DC-DC converter subject to load and input voltage disturbances, using the proposed fuzzy controller are provided to illustrate the effectiveness of the proposed approach.

关键词： Power electronics, supply and supervisory circuits Tagaki-Sugeno fuzzy model stability Stability in control theory stability analysis Fuzzy control Nonlinear control systems Lyapunov theory switching convertors fuzzy-model-based control system nonlinear design methodology Lyapunov methods nonlinear control stable fuzzy controller linear algebra (numerical analysis) nonlinear control systems fuzzy control membership function condition linear matrix inequalities switching DC-DC converter fuzzy membership function switching converter

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Efficient iterative method for solving the second-order Sylvester matrix equation EVF²-AVF-CV=BW

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IET CONTROL theory AND applications 2009年第10期3卷 1401-1408页

作者： Dehghan, M. Hajarian, M. Amir Kabir Univ Technol Dept Appl Math Fac Math & Comp Sci Tehran 15914 Iran

The second-order Sylvester matrix equation EVF2 - AVF - CV = BW (including the generalised Sylvester matrix equation, normal Sylvester matrix equation and Lyapunov matrix equation as special cases) over unknown matrix pair [V, W], has wide applications in many fields. In the present study, the authors propose an iterative method to solve the second-order Sylvester matrix equation. The proposed iterative method does not depend on the Jordan form of the matrix F. By this iterative method, the solvability of the matrix equation can be determined automatically over unknown matrix pair [V, W] not equal 0. When the matrix equation is solvable, its solution pair can be obtained within finite iterative steps, and its least Frobenius norm solution pair can be obtained by choosing suitable initial matrix pair. Furthermore, its optimal approximation solution pair to a given matrix pair can be derived by finding the least norm solution pair of a new matrix equation. A numerical example is given to show the efficiency of the proposed method.

关键词： matrix algebra Interpolation and function approximation (numerical analysis) optimal approximation solution pair finite iterative method linear algebra (numerical analysis) second-order Sylvester matrix equation unknown matrix pair least Frobenius norm approximation theory initial matrix pair iterative methods numerical approximation and analysis

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Computing the controllability radius: a semi-definite programming approach

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IET CONTROL theory AND applications 2009年第6期3卷 654-660页

作者： Dumitrescu, B. Sicleru, B. C. Stefan, R. Univ Politehn Bucuresti Dept Automat Control & Comp Bucharest 060042 Romania Tampere Univ Technol Tampere Int Ctr Signal Proc FIN-33101 Tampere Finland

A semi-definite programming (SDP) approach to compute the controllability radius is proposed in this paper. The initial nonconvex optimisation problem is transformed into the minimisation of the smallest eigenvalue of a bivariate real or trigonometric polynomial with matrix coefficients. A sum-of-squares relaxation leads to the SDP formulation. A similar technique is used for the computation of the stabilisability radius. The approach is extended to the computation of the worst-case controllability radius for systems that depend polynomially on a small number of parameters. Experimental results show that the proposed methods compete well with previous ones in a complexity/accuracy trade-off.

关键词： worst-case controllability radius Optimisation techniques eigenvalues and eigenfunctions controllability stability trigonometric polynomial Stability in control theory linear algebra (numerical analysis) sum-of-square relaxation smallest bivariate real eigenvalue minimisation stabilisability radius concave programming matrix coefficient semidefinite programming nonconvex optimisation problem polynomial matrices

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Matrices, Moments and Quadrature with applications (Princeton Series in Applied Mathematics)

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丛书名： Princeton Series in Applied Mathematics

2009年

作者： Gene H. Golub Gerard Meurant

ISBN: (数字)9781400833887

ISBN: (纸本)9780691143415

This computationally oriented book describes and explains the mathematical relationships among matrices, moments, orthogonal polynomials, quadrature rules, and the Lanczos and conjugate gradient algorithms. The book bridges different mathematical areas to obtain algorithms to estimate bilinear forms involving two vectors and a function of the matrix. The first part of the book provides the necessary mathematical background and explains the theory. The second part describes the applications and gives numerical examples of the algorithms and techniques developed in the first *** addressed in the book include computing elements of functions of matrices; obtaining estimates of the error norm in iterative methods for solving linear systems and computing parameters in least squares and total least squares; and solving ill-posed problems using Tikhonov *** book will interest researchers in numerical linear algebra and matrix computations, as well as scientists and engineers working on problems involving computation of bilinear forms.

关键词： Mathematics Matrices

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Preservation of linear Constraints in Approximation of Tensors

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numerical Mathematics(theory,methods and applications) 2009年第4期2卷 421-426页

作者： Eugene Tyrtyshnikov Institute of Numerical Mathematics of Russian Academy of Sciences

For an arbitrary tensor(multi-index array) with linear constraints at each direction,it is proved that the factors of any minimal canonical tensor approximation to this tensor satisfy the same linear constraints for t... 详细信息

关键词： Multi-index arrays tensors linear constraints low rank approximation canonicaltensor decomposition multilevel matrices.

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Observer-based resilient L₂-L_∞ control for singular time-delay systems

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IET CONTROL theory AND applications 2009年第10期3卷 1351-1362页

作者： Li, L. Jia, Y. Beihang Univ Dept Syst & Control Beijing 100191 Peoples R China

The problem of non-fragile (or resilient) L-2-L-infinity control for a class of singular systems with time-varying delay is considered via observer-based state feedback control. The objective is to design an observer-based feedback controller with additive gain variations such that, for all admissible observer and controller gain variations, the closed-loop system is regular, impulse free and stable with a prescribed L-2-L-infinity performance index satisfied. In terms of linear matrix inequalities, a new delay-dependent stability criterion is derived. Based on the obtained criterion, the non-fragile observer and controller design method is proposed. numerical example and simulation results are included to show the effectiveness of the proposed results.

关键词： performance index feedback controller design nonfragile L2-L∞ control time-varying systems Time-varying control systems stability control system synthesis Stability in control theory Control system analysis and synthesis methods state feedback state feedback control closed loop systems algebra resilient L2-L∞ control delay-dependent stability criterion time-varying delay linear matrix inequalities observer L2-L∞ performance index closed-loop system observers additive gain variations Simulation, modelling and identification Distributed parameter control systems delay systems singular time-delay systems

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On Superlinear PCG methods for FDM Discretizations of Convection-Diffusion Equations

On Superlinear PCG Methods for FDM Discretizations of Convec...

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4th International conference on numerical Analysis and applications

作者： Karatson, Janos Kurics, Tamas ELTE Univ Dept Appl Anal & Computat Math H-1117 Budapest Hungary

ISBN: (纸本)9783642004636

The numerical solution of linear convection-diffusion equations is considered. Finite difference discretization leads to an algebraic system solved by a suitable preconditioned CC method, where the preconditioning approach is based on equivalent operators. Our goal is to study the superlinear convergence of the preconditioned CC iteration and to find mesh independent behaviour on a model problem. This is an analogue of previous results where FEM discretization was used.

关键词： algebra

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Non-solvable groups are not in FO+MOD+M - AJ2[REG]

Non-solvable groups are not in FO+MOD+M - AJ2[REG]

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3rd International conference on Language and Automata theory and applications, LATA 2009

作者： Behle, Christoph Krebs, Andreas Reifferscheid, Stephanie WSI - University of Tübingen Sand 13 72076 Tübingen Germany

ISBN: (纸本)9783642009815

Motivated by the open question whether TC0 = NC1 we consider the case of linear size TC0. We use the connections between circuits, logic, and algebra, in particular the characterization of TC 0 in terms of finitely typed monoids. Applying algebraic methods we show that the word problem for finite non-solvable groups cannot be described by a FO+MOD+MAJ[REG] formula using only two variables. This implies a separation result of FO[REG]-uniform linear TC0 from linear NC1. © Springer-Verlag Berlin Heidelberg 2009.

关键词： algebra

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Special Issue for Image Processing and numerical linear algebra

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numerical Mathematics(theory,methods and applications) 2009年第4期 5-6页

作者： Michael K.Ng Eugene Tyrtyshnikov Department of Mathematics and Centre for Mathematical Imaging and Vision Hong Kong Baptist University Institute of Numerical Mathematics of the Russian Academy of Sciences and Institute for Computational Mathematics Hong Kong Baptist University

The Third International conference on Scientific Computing and Partial Differential Equations(SCPDE) was held from December 8 to December 12,2008 at Hong Kong Baptist *** was a sequel to similar conferences held in Hong Kong(2002 and 2005). The conference aims to promote research interests in scientific *** SCPDE 2008,two workshops on image processing and numerical linear algebra are organized to review recent scientific developments and explore exciting new directions in mathematical modeling and computational methods in these two *** are twenty one invited speakers in these two workshops(http://***/SCPDE08/).

关键词： Special Issue for Image Processing and numerical linear algebra

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Stability Criterions for Switched linear Systems Based on Matrix Measure

Stability Criterions for Switched Linear Systems Based on Ma...

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4th IEEE conference on Industrial Electronics and applications

作者： Zou, Hongbo Li, Han Xu, Ouguan Hangzhou Dianzi Univ Inst Informat & Control Hangzhou 310018 Zhejiang Peoples R China China Bldg Tech Grp Co Ltd Inst Design 3 Beijing 100013 Peoples R China Zhejiang Univ Technol Hangzhou 310024 Peoples R China

ISBN: (纸本)9781424427994

The problem of stability analysis for a class of switched linear systems is studied in this paper based on the theory of matrix measure. The matrix measures of all subsystems are used to determine the stability of the switched linear systems. Based on this, sufficient conditions are reached, which can be used to determine the stability or instability of switched linear systems under arbitrary switching law. If a switching sequence satisfies some conditions, a theorem in this paper can be used to verify if it can stabilize the systems. The obtained conditions are simpler than the reported methods such as multi-Lyapunov functions and hence are easier to check. numerical examples are used to demonstrate these conditions.

关键词： Hybrid systems Switched Systems Matrix Measure

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