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Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign

IET CONTROL theory AND applications 2009年第8期3卷 1070-1080页

作者： Kim, D. W. Park, J. B. Joo, Y. H. Yonsei Univ Dept Elect & Elect Engn Seoul 120749 South Korea Kunsan Natl Univ Sch Elect & Informat Engn Kunsan 573701 Chonbuk South Korea

This study addresses a new digital redesign (DR) problem for a linear time-invariant (LTI) system with a perturbation that is an uncertain non-linear time-varying function but linearly bounded. Given a continuous-time linear controller robustly stabilising the origin of the perturbed system for all admissible perturbations, the concerned DR problem is to design the sampled-data linear controller making trajectories of the continuous-time and the sampled-data non-linear control systems close, or at least robustly stabilising the perturbed system. The proposed approach interprets the DR problem as the stabilisation problem considering the convergence rate for error dynamics between the continuous-time and the sampled-data non-linear control systems. Sufficient conditions for the stabilisation are derived and formulated in the form of linear matrix inequalities (LMIs). A numerical example is used to demonstrate the effectiveness of the proposed design technique.

关键词： convergence rate sampled-data control systems nonlinear perturbations perturbation techniques time-varying systems Time-varying control systems Stability in control theory control system synthesis digital redesign problem error dynamics Control system analysis and synthesis methods Nonlinear control systems continuous-time linear controller linear systems robust control algebra uncertain nonlinear time-varying function linear time-invariant system nonlinear control systems continuous time systems uncertain systems linear matrix inequalities Discrete control systems robust stabilisation sampled data systems sampled-data nonlinear control systems

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A class of approximate inverse preconditioners for solving linear systems

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2009年第7期86卷 1243-1252页

作者： Zhang, Yong Huang, Ting-Zhu Liu, Xing-Ping Gu, Tong-Xiang Univ Elect Sci & Technol China Sch Appl Math Chengdu 610054 Sichuan Peoples R China Inst Appl Phys & Computat Math Lab Computat Phys Beijing 100088 Peoples R China

Some preconditioners for accelerating the classical iterative methods are given in Zhang et al. [Y. Zhang and T.Z. Huang, A class of optimal preconditioners and their applications, Proceedings of the Seventh International conference on Matrix theory and Its applications in China, 2006. Y. Zhang, T.Z. Huang, and X.P. Liu, Modified iterative methods for nonnegative matrices and M-matrices linear systems, Comput. Math. Appl. 50 (2005), pp. 1587-1602. Y. Zhang, T.Z. Huang, X.P. Liu, A class of preconditioners based on the (I+S())-type preconditioning matrices for solving linear systems, Appl. Math. Comp. 189 (2007), pp. 1737-1748]. Another kind of preconditioners approximating the inverse of a symmetric positive definite matrix was given in Simons and Yao [G. Simons, Y. Yao, Approximating the inverse of a symmetric positive definite matrix, linear algebra Appl. 281 (1998), pp. 97-103]. Zhang et al. 's preconditioners and Simons and Yao's are generalized in this paper. These preconditioners are all of low construction cost, which all could be taken as approximate inverse of M-matrices. numerical experiments of these preconditioners applied with Krylov subspace methods show the effectiveness and performance, which also show that the preconditioners proposed in this paper are better approximate inverse for M-matrices than Simons'.

关键词： preconditioning M-matrix Krylov subspace method sparse approximate inverse

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A delay-partitioning projection approach to stability analysis of continuous systems with multiple delay components

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IET CONTROL theory AND applications 2009年第4期3卷 383-390页

作者： Du, B. Lam, J. Shu, Z. Wang, Z. Univ Hong Kong Dept Mech Engn Hong Kong Hong Kong Peoples R China Brunel Univ Dept Informat Syst & Comp Uxbridge UB8 3PH Middx England

An effective approach is introduced to study the stability of continuous systems with multiple time-varying delay components. By employing a new Lyapunov-Krasovskii functional form based on delay partitioning, delay-dependent stability criteria are established for cases with or without the information of the delay rates. The contribution of the paper is 2-fold. First, it provides an improvement, as well as generalisation, of the existing stability criteria for continuous systems with multiple time-varying delay components. Second, it is illustrated numerically that the approach can be applied to estimate the delay bound for system stability in the single delay case with reduction both in conservatism and computational complexity when compared with the existing methods.

关键词： delay-partitioning projection approach linear systems multiple time-varying delay component Time-varying control systems computational complexity stability Stability in control theory Lyapunov-Krasovskii functional form Computational complexity delay bound estimation delays linear algebra (numerical analysis) matrix parameter continuous systems Distributed parameter control systems linear continuous system stability analysis Lyapunov matrix equations time-varying systems

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New results on the approximate solution of the non-linear partial derivative equation system of corona-electrostatic separation

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KYBERNETES 2009年第5期38卷 762-779页

作者： Caron, Armand IUT Lorient Dept QLIO Lorient France Univ Bretagne Sud LIMAT Lab Ingn MATeriaux Lorient France

Purpose - The purpose of this paper is to add precisions to a method. to demonstrate the convergence, to explain time and memory space complexities and new simulated results on a non-linear partial derivative equation system governing corona-electrostatic electric field for granular mixture separation. Design/methodology/approach - The method converts the non-linear partial derivative system into an iterative system of linear equations. Using the well-known finite difference approximation, a numerical solution is computed very quickly. Findings - The paper gives the truncated error and the approximation error to conclude to the convergence. Originality/value - The paper shows the fast numerical solution leads to confidence in the numerical approximations for the comprehension of the phenomenon. Extends the corona-electrostatic electric field for granular mixture separation to new geometries easily.

关键词： Cybernetics Research Approximation theory Electrostatics

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Stability Feeler: a tool for parametric robust stability analysis and its applications

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IET CONTROL theory AND applications 2009年第12期3卷 1625-1633页

作者： Matsuda, T. Mori, T. Toyota Technol Inst Tempaku Ku Nagoya Aichi 4688511 Japan Kyoto Inst Technol Sakyo Ku Kyoto 6068585 Japan

In this study the authors propose a new tool for robust stability analysis. This tool gives D-stability intervals along a given line in the polynomial coefficient space. D-stability means that all the zeros of characteristic polynomials are in a prescribed connected open region and therefore, besides continuous-time systems or discrete-time systems, any systems having such a pole location can be analysed by utilising this tool. The tool is referred to as 'Stability Feeler', named after a feeler of insects. It is shown that Stability Feeler can be systematically computed by using standard numerical calculations. The authors also show two applications of Stability Feeler. One is the design of robust controllers for linear uncertain systems. The other is robust absolute stability analysis of Lur'e systems. For the robust controller design, it is often necessary to analyse stability of systems with the designed controllers. However, by the support of Stability Feeler, the authors can directly obtain a class of stabilising controllers. For robust absolute stability of interval Lur'e systems, a sufficient condition has already been proposed, while Stability Feeler enables one to analyse stability of both continuous-time and discrete-time Lur'e systems with affine linear uncertainties, which are more general than interval ones. Moreover, sharpness of any robust absolute stability criteria for uncertain Lur'e systems can be assessed.

关键词： linear uncertain systems robust absolute stability analysis Lur`e systems stability Stability in control theory Control system analysis and synthesis methods polynomials linear systems continuous-time systems algebra stability feeler poles and zeros polynomial zeros continuous time systems uncertain systems parametric robust stability analysis Discrete control systems polynomial coefficient space pole location discrete-time systems discrete time systems D-stability intervals

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Robust generalised H₂ and H_∞ static output feedback control for uncertain discrete-time fuzzy systems

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IET CONTROL theory AND applications 2009年第7期3卷 865-876页

作者： Zhang, J. Xia, Y. Mahmoud, M. S. Beijing Inst Technol Dept Automat Control Beijing 100081 Peoples R China King Fahd Univ Petr & Minerals Dept Syst Engn Dhahran 31261 Saudi Arabia

This study is concerned with the generalised H-2 and the H-infinity static control problems for discrete-time fuzzy systems with time-varying norm-bounded parametric uncertainties. Based on the solutions to certain linear matrix inequalities LMIs, static output feedback controllers are designed, which can ensure the asymptotic stability and the generalised H-2 and H-infinity performance level, respectively. Differenting from the existing results, the design conditions in this study are derived in terms of LMIs directly, and the local output matrices are allowed to be different. Three illustrative examples are provided to demonstrate the effectiveness and the reduced conservatism of the proposed methods.

关键词： H∞ control robust generalised H2 static output feedback control time-varying systems Time-varying control systems time-varying norm-bounded parametric uncertainty Stability in control theory control system synthesis linear matrix inequality Control system analysis and synthesis methods Fuzzy control fuzzy systems uncertain discrete-time fuzzy system robust control feedback linear algebra (numerical analysis) fuzzy control Optimal control linear matrix inequalities Discrete control systems discrete time systems asymptotic stability

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

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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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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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numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form

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numerical linear algebra WITH applications 2009年第1期16卷 63-86页

作者： Mackey, D. Steven Mackey, Niloufer Mehl, Christian Mehrmann, Volker Tech Univ Berlin Inst Math D-10623 Berlin Germany Western Michigan Univ Dept Math Kalamazoo MI 49008 USA Univ Birmingham Sch Math Birmingham B15 2TT W Midlands England

We present structure-preserving numerical methods for the eigenvalue problem of complex palindromic pencils. Such problems arise in control theory, as well as from palindromic linearizations of higher degree palindromic matrix polynomials. A key ingredient of these methods is the development of an appropriate condensed form-the anti-triangular Schur form. Ill-conditioned problems with eigenvalues near the unit circle, in particular near +/- 1, are discussed. We show how a combination of unstructured methods followed by a structured refinement can be used to solve such problems accurately. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： nonlinear eigenvalue problem palindromic matrix polynomial palindromic pencil Schur form anti-triangular form Jacobi algorithm structured deflation method palindromic QR-algorithm

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