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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)

- Mihail Konstantinov, Petko Hr. Petkov, Nicolai Christov
- Kybernetika
- 1993

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.

- Mihail Konstantinov, Petko Hr. Petkov
- SIAM J. Matrix Analysis Applications
- 1999

- Mihail Konstantinov, Volker Mehrmann, Petko Hr. Petkov
- SIAM J. Matrix Analysis Applications
- 2001

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)

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)

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)

- Mihail Konstantinov, Petko Hr. Petkov, Nicolai Christov
- SIAM J. Scientific Computing
- 1990

- Mihail Konstantinov, Petko Hr. Petkov, Nikolai D. Christov
- Kybernetika
- 1981

Subject of the present paper is the study and construction of complete independent invariants and canonical forms for linear multivariable systems under the action of orthogonal transformation groups. Stable computational algorithms for finding the orthogonal canonical forms are presented and their numerical properties are discussed. In view of their nice… (More)

- Petko Hr. Petkov, Nicolai Christov, Mihail Konstantinov
- ACM Trans. Math. Softw.
- 1984

The subroutine EXCHQZ cannot interchange 2 × 2 blocks when the first block corresponds to infinite generalized eigenvalues. I The generalized eigenvalues of the first 2 × 2 block of the corresponding pencil are infinite while these of the second block are 5 _+. 5i. When an attempt is made to interchange the blocks the shifts used in the double QZ step… (More)

The Linear-Quadratic Gaussian (LQG) design is the most efficient and widely used design approach in the field of linear stochastic control systems. From theoretical point of view this approach is reduced to the synthesis of a LQ state regulator and of a Kalman filter for the controlled system. From computational point of view the LQG design consists of… (More)