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The LMI control toolbox
TLDR
This paper describes a new MATLAB-based toolbox for control design via linear matrix inequality (LMI) techniques, and its contents and capabilities are presented.
The singular value decomposition: Its computation and some applications
We provide a tutorial introduction to certain numerical computations both in linear algebra and linear systems in the context of bounded arithmetic. The essential characteristics of bounded
A schur method for solving algebraic Riccati equations
  • A. Laub
  • Mathematics
    IEEE Conference on Decision and Control including…
  • 1978
In this paper a new algorithm for solving algebraic Riccati equations (both continuous-time and discrete-time versions) is presented. The method studied is a variant of the classical eigenvector
Matrix analysis - for scientists and engineers
  • A. Laub
  • Mathematics, Computer Science
  • 29 December 2004
TLDR
This book discusses vector spaces, linear transformations, eigenvalues and eigenvectors, and the singular value decomposition in the context of Kronecker products.
Generalized eigenproblem algorithms and software for algebraic Riccati equations
Numerical issues related to the computational solution of the algebraic matrix Riccati equation are discussed. The approach presented uses the generalized eigenproblem formulation for the solution of
Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
An algorithm is presented in this paper for computing state-space balancing transformations directly from a state-space realization. The algorithm requires no "squaring up" or unnecessary matrix
The linear-quadratic optimal regulator for descriptor systems
  • D. Bender, A. Laub
  • Mathematics, Computer Science
    24th IEEE Conference on Decision and Control
  • 1985
Numerical solution of the discrete-time periodic Riccati equation
  • J. Hench, A. Laub
  • Computer Science, Mathematics
    IEEE Trans. Autom. Control.
  • 1 June 1994
TLDR
This method simultaneously triangularizes by orthogonal equivalences a sequence of matrices associated with a cyclic pencil formulation related to the Euler-Lagrange difference equations to extract a basis for the stable deflating subspace of the extended pencil, from which the Riccati solution is obtained.
Small-Sample Statistical Condition Estimates for General Matrix Functions
A new condition estimation procedure for general matrix functions is presented that accurately gauges sensitivity by measuring the effect of random perturbations at the point of evaluation. In this
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