The study of matrix inequalities in a dimension-free setting is in the realm of free real algebraic geometry (RAG). In this paper we investigate constrained trace and eigenvalue optimization of noncommutative polynomials. We present Lasserre’s relaxation scheme for trace optimization based on semidefinite programming (SDP) and demonstrate its convergence properties. Finite convergence of this r...

In this paper, we introduce the concept of x-maximal flatness. A control system is x-maximally flat if the number of new states gained by each successive derivation of the flat output is the largest possible. Firstly, we show that the only control-linear systems that are xmaximally flat are those that are static feedback equivalent to the m-chained form. Secondly, we generalize that result from...

The average concentration of tracers advected from a point source by a multivariate normal velocity field is shown to deviate from a Gaussian profile. The flatness ~kurtosis! is calculated using an asymptotic series expansion valid for velocity fields with short correlation times or weak space dependence. An explicit formula for the excess flatness at first order demonstrates maximum deviation ...

We show that ( n + 1)-dimensional Myers–Perry metrics, ≥ 4, have a conformal completion at space-like infinity of C n−3,1 differentiability class and the result is optimal in even spacetime dimensions. The associated asymptotic symmetries are presented.

This paper studies a formation control problem for nonlinear multi-agent systems; specifically non-holonomic vehicles represented as linear parameter-varying (LPV) models are of interest here. The objective of this study is twofold. First, we demonstrate the applicability of a novel approach to distributed control for LPV decomposable systems (Hoffmann et al., 2013). Second, we investigate diff...