It is well-known that many factors contribute to the accurate and efficient numerical solution of mathematical problems such as those arising in computational control system design. In simple terms these are the arithmetic of the machine on which the calculations are carried out, sensitivity (or conditioning) of the mathematical model to small changes of… (More)
lthough numerical methods have been used for many centuries to solve problems in science and engineering, the importance of computation grew tremendously with the advent of digital computers. It became immediately clear that many of the classical analytical and numerical methods and algorithms could not be implemented directly as computer codes, although… (More)
The sensitivity of the discrete-time matrix Riccati equation relative to perturbations in its coefficients is studied. Both local and non-local perturbation bounds are obtained. In particular the conditioning of the equation is determined.
In this paper we present a complete perturbation analysis for the Hamiltonian Schur form of a Hamiltonian matrix under similarity transformations with unitary symplectic matrices. Both linear asymptotic and non-linear perturbation bounds are presented. The same analysis is also carried out for two less condensed block-Schur forms. It suggests that the block… (More)
The paper is devoted to the perturbation theory for defective matrices. We consider the asymptotic expansions of the perturbed spectrum when a matrix A is changed to A+tE, where E 6 = 0 and t > 0 is a small parameter. In particular we analyse the rational exponents that may occur when the matrix E varies over the sphere kEk = > 0. We partially characterize… (More)
We study the sensitivity of the solution of a general type matrix equation Q ± A H X p A − X = 0. Local and nonlocal perturbation bounds are derived. The results are obtained using the technique of Lyapunov majorants and fixed point principles. A numerical example is given.
Preface With the ever-increasing complexity of control systems, efficient computational methods for their analysis and design are becoming more and more important. These computational methods need to be based on reliable and robust numerical software provided by well-tested and user-friendly software libraries. This workshop is intended as a tutorial on… (More)