Positive polynomial matrices and linear matrix inequalities (LMI) can be used to design linear parameter varying (LPV) controllers depending polynomially on the scheduling parameters, and robust to polynomial parametric uncertainty. The salient features of the approach are (a) the ability to design a controller of order and structure fixed a priori; (b) the use of a transfer function, or polyno...

1.1 Abstract An approach for solving nonlinear polynomial equations involving parameters is proposed. A distinction is made between parameters and variables. The objective is to generate from a system of parametric equations, solved forms from which solutions for speciic values of parameters can be obtained without much additional computations. It should be possible to analyze the parametrized ...

Given the equations of the first and the second order surfaces in Rn, our goal is to construct a univariate polynomial one of the zeros of which coincides with the square of the distance between these surfaces. To achieve this goal we employ Elimination Theory methods. The proposed approach is also extended for the case of parameter dependent surfaces.

We study the Travelling Salesperson (TSP) and Steiner Tree problem (STP) in graphs of low highway dimension. This graph parameter roughly measures how many central nodes are visited by all shortest paths a certain length. It has been shown that transportation networks, on which TSP STP naturally occur for various applications logistics, typically have small While it was previously these problem...