Jaroslav Kautsky

Robust pole assignment in linear state feedback

Numerical methods are described for determining robust, or well-conditioned, solutions to the problem of pole assignment by state feedback. The solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized. It is shown that for these solutions, upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized. A measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed-loop poles, and hence the suitability of the given poles for assignment.

A new wavelet-based measure of image focus

We present a new measure of image focus. It is based on wavelet transform of the image and is defined as a ratio of high-pass band and low-pass band norms. We show this measure is monotonic with respect to the degree of defocusation and sufficiently robust. We experimentally illustrate its performance on simulated as well as real data and compare it with existing focus measures (gray-level variance and energy of Laplacian). Finally, an application of the new measure in astronomical imaging is shown.

Eigenstructure assignment in descriptor systems

Coordinate free conditions are given for pole assignment by feedback in linear descriptor (singular) systems which guarantee closed-loop regularity. These conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles. Transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Equidistributing Meshes with Constraints

Adaptive methods which “equidistribute” a given positive weight function are now used fairly widely for selecting discrete meshes. The disadvantage of such schemes is that the resulting mesh may not be smoothly varying. In this paper a technique is developed for equidistributing a function subject to constraints on the ratios of adjacent steps in the mesh. Given a weight function

Robust pole assignment in singular control systems

f \geqq 0

Calculation of Gauss quadratures with multiple free and fixed knots

on an interval

On the calculation of Jacobi Matrices

[a,b]

Robust detection of significant points in multiframe images

and constants c and K, the method produces a mesh with points

Smoothed histogram modification for image processing

x_0 = a,x_{j + 1} = x_j + h_j ,j = 0,1, \cdots ,n - 1