Analytic perturbation of Sylvester and Lyapunov matrix equations
We consider an analytic perturbation of the Sylvester matrix equation. Mainly we are interested in the singular case, that is, when the null space of the unperturbed Sylvester operator is not trivial, but the perturbed equation has a unique solution. In this case, the solution of the perturbed equation can be given in terms of a Laurent series. We provide a necessary and sufficient condition for the existence of a Laurent series with a first order pole. An efficient recursive procedure for the calculation of the Laurent series' coefficients is given. Finally, we show that in the particular, but practically important case of semisimple eigenvalues, the recursive procedure can be written in a compact matrix form.
A new approach of robust observer design
This paper shows that based on the recent development of observer design solution, an observer pole selection method can be formulated to minimize the observer gain to the system input. It is proved in this paper that this method is a deterministic approach of the recovery, of loop transfer function and robustness of direct state feedback system.
Synthesis of quasi-stationary inhomogeneous impedance body of arbitrary shape
Formulas were obtained for the reflection factors of a plane wave from the inhomogeneous impedance plane, which reflects the incident wave in the given direction. The problem of synthesis of impedance inhomogeneous rotation body was solved for an arbitrary shaped generatrix for the given scattering diagram for co- and cross polarizations. Impedance distributions were obtained in explicit form. Restrictions on the class of implementable scat- terplots were formulated.