A State-Space Approach to Parametrization of Stabilizing Controllers for Nonlinear Systems

A state-space approach to Youla-parametrization of stabilizing controllers for linear and nonlinear systems is suggested. The stabilizing controllers (or a class of stabilizing controllers for nonlinear systems) are characterized as (linear/nonlinear) fractional transformations of stable parameters. The main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems. The parametrized output feedback controllers have separation structures. A separation principle follows from the construction. This machinery allows the parametrization of stabilizing controllers to be conducted directly in state space without using coprime-factorization

Geometric transport along circular orbits in stationary axisymmetric spacetimes

Parallel transport along circular orbits in orthogonally transitive stationary axisymmetric spacetimes is described explicitly relative to Lie transport in terms of the electric and magnetic parts of the induced connection. The influence of both the gravitoelectromagnetic fields associated with the zero angular momentum observers and of the Frenet-Serret parameters of these orbits as a function of their angular velocity is seen on the behavior of parallel transport through its representation as a parameter-dependent Lorentz transformation between these two inner-product preserving transports which is generated by the induced connection. This extends the analysis of parallel transport in the equatorial plane of the Kerr spacetime to the entire spacetime outside the black hole horizon, and helps give an intuitive picture of how competing "central attraction forces" and centripetal accelerations contribute with gravitomagnetic effects to explain the behavior of the 4-acceleration of circular orbits in that spacetime.Comment: 33 pages ijmpd latex article with 24 eps figure

Consistency of LCDM with Geometric and Dynamical Probes

The LCDM cosmological model assumes the existence of a small cosmological constant in order to explain the observed accelerating cosmic expansion. Despite the dramatic improvement of the quality of cosmological data during the last decade it remains the simplest model that fits remarkably well (almost) all cosmological observations. In this talk I review the increasingly successful fits provided by LCDM on recent geometric probe data of the cosmic expansion. I also briefly discuss some emerging shortcomings of the model in attempting to fit specific classes of data (eg cosmic velocity dipole flows and cluster halo profiles). Finally, I summarize recent results on the theoretically predicted matter overdensity ($\delta_m=\frac{\delta \rho_m}{\rho_m}$) evolution (a dynamical probe of the cosmic expansion), emphasizing its scale and gauge dependence on large cosmological scales in the context of general relativity. A new scale dependent parametrization which describes accurately the growth rate of perturbations even on scales larger than 100h^{-1}Mpc is shown to be a straightforward generalization of the well known scale independent parametrization f(a)=\omms(a)^\gamma valid on smaller cosmological scales.Comment: 20 pages, 6 figures. Invited review at the 1st Mediterranean Conference on Classical and Quantum Gravity (MCCQG). To appear in the proceeding