The LMI control toolbox
- P. Gahinet, A. Nemirovskii, A. Laub, M. Chilali
- MathematicsProceedings of 33rd IEEE Conference on Decision…
- 14 December 1994
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
This work provides a tutorial introduction to certain numerical computations both in linear algebra and linear systems in the context of bounded arithmetic and the singular value decomposition (SVD).
A schur method for solving algebraic Riccati equations
- A. Laub
- Mathematics, Computer ScienceIEEE Conference on Decision and Control including…
A new algorithm for solving algebraic Riccati equations (both continuous-time and discrete-time versions) is presented, a variant of the classical eigenvector approach and uses instead an appropriate set of Schur vectors thereby gaining substantial numerical advantages.
Matrix analysis - for scientists and engineers
- A. Laub
- 29 December 2004
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
The approach presented uses the generalized eigenproblem formulation for the solution of general forms of algebraic Riccati equations arising in both continuous- and discrete-time applications.
The linear-quadratic optimal regulator for descriptor systems
Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms
It is shown that a similar approach may be taken, involving the generalized singular value decomposition of a certain product of matrices without explicitly forming the product, to the classical simultaneous diagonalization problem.
Numerical solution of the discrete-time periodic Riccati equation
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…