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Coefficient matrix
About: Coefficient matrix is a research topic. Over the lifetime, 7184 publications have been published within this topic receiving 151879 citations.
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TL;DR: In this article, simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: for a given number gamma > 0, find all controllers such that the H/ sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma.
Abstract: Simple state-space formulas are derived for all controllers solving the following standard H/sub infinity / problem: For a given number gamma >0, find all controllers such that the H/sub infinity / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma /sup 2/. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H/sub 2/) theory. This paper is intended to be of tutorial value, so a standard H/sub 2/ solution is developed in parallel. >
5,272 citations
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24 May 2010TL;DR: The author presents Perron-Frobenius theory of nonnegative matrices Index, a theory of matrices that combines linear equations, vector spaces, and matrix algebra with insights into eigenvalues and Eigenvectors.
Abstract: Preface 1. Linear equations 2. Rectangular systems and echelon forms 3. Matrix algebra 4. Vector spaces 5. Norms, inner products, and orthogonality 6. Determinants 7. Eigenvalues and Eigenvectors 8. Perron-Frobenius theory of nonnegative matrices Index.
4,979 citations
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31 Dec 1968TL;DR: In this article, the authors introduce a system of linear and quasi-linear equations with principal part in divergence (PCI) in the form of systems of linear, quasilinear and general systems.
Abstract: Introductory material Auxiliary propositions Linear equations with discontinuous coefficients Linear equations with smooth coefficients Quasi-linear equations with principal part in divergence form Quasi-linear equations of general form Systems of linear and quasi-linear equations Bibliography.
3,986 citations
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TL;DR: In this paper, a relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described, where the GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations.
Abstract: A computationally efficient relocatable system for generalized inverse (GI) modeling of barotropic ocean tides is described. The GI penalty functional is minimized using a representer method, which requires repeated solution of the forward and adjoint linearized shallow water equations (SWEs). To make representer computations efficient, the SWEs are solved in the frequency domain by factoring the coefficient matrix for a finite-difference discretization of the second-order wave equation in elevation. Once this matrix is factored representers can be calculated rapidly. By retaining the first-order SWE system (defined in terms of both elevations and currents) in the definition of the discretized GI penalty functional, complete generality in the choice of dynamical error covariances is retained. This allows rational assumptions about errors in the SWE, with soft momentum balance constraints (e.g., to account for inaccurate parameterization of dissipation), but holds mass conservation constraints. Wh...
3,133 citations
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01 Aug 1997TL;DR: The symmetric Eigenproblem and singular value decomposition and the Iterative methods for linear systems Bibliography Index.
Abstract: Preface 1. Introduction 2. Linear equation solving 3. Linear least squares problems 4. Nonsymmetric Eigenvalue problems 5. The symmetric Eigenproblem and singular value decomposition 6. Iterative methods for linear systems 7. Iterative methods for Eigenvalue problems Bibliography Index.
2,983 citations