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L. Fletcher

Bio: L. Fletcher is an academic researcher from University of Salford. The author has contributed to research in topics: Matrix (mathematics) & Eigenvalues and eigenvectors. The author has an hindex of 3, co-authored 4 publications receiving 160 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity, and these conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles.
Abstract: Coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity. These conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles. Transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback.

104 citations

Journal ArticleDOI
TL;DR: In this paper, necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented, where the concept of inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigen structure consisting of the eigenvalues and a mixture of left and right eigenvectors.
Abstract: Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.

51 citations

Book ChapterDOI
01 Jan 1983
TL;DR: The state feedback pole assignment problem in control system design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf. as discussed by the authors ), and a number of formally constructive methods for eigen value assignment by feedback are described in the literature, but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem.
Abstract: The state feedback pole assignment problem in control system design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf Fletcher, in these proceedings) A number of formally constructive methods for eigenvalue assignment by feedback are described in the literature [13] [11], [1], but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem, that is, to solutions which are insensitive to perturbations in the system Stable numerical methods for inverse eigenvalue problems have been developed in other contexts (compare for instance, references [2], [5], [6]), but these procedures are designed to handle only very specific classes of matrices and are not directly applicable to the forms arising in control theory

8 citations

01 Jan 1983
TL;DR: In this article, the authors describe algorithms for computing solutions to the pole assignment problem which satisfy certain robustness criteria, which guarantee that the assi~ned eigenvalues are as insensitive to perturbations as is feasible, and also that the resulting feedback matrix and corresponding transient response are as reasonably bounded as may be expected, given the original system.
Abstract: design is essentially an inverse eigenvalue problem, which requires the determination of a matrix having given eigenvalues (cf. Fletcher, in these proceedings). A number of formally constructive methods for eigenvalue assignment by feedback are described in the literature ,13J OlJ, 11 J, but these procedures are not in general stable for numerical computation, and do not necessarily lead to robust, or well-conditioned, solutions of the problem, that is, to solutions which are insensitive to perturbations in the system. Stable numerical methods for inverse eigenvalue problems have been developed in other contexts (compare for instance, references '2], '5J, [6J), but these procedures are desi~ned to handle only very specific classes of matrices and are not directly applicable to the forms arising in control theory. The basic difficulty in develoning an algorithm for the inverse eigenvalue problem is that the solution is not uniquely determined. In the special case of a single-input control system, only one solution to the eigenvalue assignment problem may exist, and a numeri­ cally stable technique for computing the feedback is available [9l. For the nUlti-input problem additional criteria must be imposed to restrict the degrees of freedom in the problem. In this paper we describe algorithms for computing solutions to the pole assignment problem which satisfy certain robustness criteria. These criteria guarantee that the assi~ned eigenvalues are as insensitive to pertur­ bations as is feasible, and also that the resulting feedback matrix and corresponding transient response are as reasonably bounded as may be expected, given the original system. In the next section the pole assignment problem is defined in detail, and theoretical considerations are discussed. In Section 3 we describe the numerical al~orithm.

1 citations


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Journal ArticleDOI
TL;DR: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized.
Abstract: Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

1,035 citations

Journal ArticleDOI
TL;DR: The best concise account of the basic mathematical aspects of control has been brought completely up to date while retaining its focus on state-space methods and its emphasis on points of mathematical interest.
Abstract: The best concise account of the basic mathematical aspects of control has been brought completely up to date while retaining its focus on state-space methods and its emphasis on points of mathematical interest. The authors have written a new chapter on multivariable theory and a new appendix on Kalman filtering, added a large number of new problems, and updated all the references. This book will continue as a fundamental resource for applied mathematicians studying control theory and for control engineers and electrical and mechanical engineers pursuing mathematically oriented studies. From reviews of the first edition: \"Excellent....Strongly recommended.\"--Bulletin of the International Mathematical Association. \"Could hardly be bettered.\"--Times Higher Education Supplement

264 citations

Journal ArticleDOI
TL;DR: A complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed, and two new algorithms are presented.
Abstract: Two new simple, complete, analytical, and restriction-free solutions with complete and explicit freedom of the matrix equation AV+BW=VF are proposed. Here (AB) is known and is controllable, and F is in the Jordan form with arbitrary given eigenvalues. Based on the proposed solutions of this matrix equation, a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed, and two new algorithms are presented. The proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective. >

227 citations

Journal ArticleDOI
TL;DR: A simple complete analytical restriction-free parametric solution with complete and explicit freedom of matrix equation AV + BW = EVF is presented and an approach for eigenstructure assignment for continuous descriptor system Ex = Ax + Bu via descriptor-variable feedback u = Kx is proposed.

137 citations

Journal ArticleDOI
TL;DR: A simple, direct, complete and explicit parametric solution of the generalized Sylvester matrix equation AV+BW=EVF is proposed for matrix F in the Jordan form with arbitrary eigenvalues using the Smith canonical form of the matrix.
Abstract: A simple, direct, complete and explicit parametric solution of the generalized Sylvester matrix equation AV+BW=EVF is proposed for matrix F in the Jordan form with arbitrary eigenvalues using the Smith canonical form of the matrix [A-sE B]. The obtained solution is in a clear, neat form and may have important applications in descriptor linear system theory.

128 citations