ℋ∞ optimization with spatial constraints

A generalized ℋ∞ synthesis problem where non-euclidian spatial norms on the disturbances and output error are used is posed and solved. The solution takes the form of a linear matrix inequality. Some problems which fall into this class are presented. In particular, solutions are presented to two problems: a variant of ℋ∞ synthesis where norm constraints on each component of the disturbance can be imposed, and synthesis for a certain class of robust performance problems

Status Report of the GERDA Phase II Startup

The GERmanium Detector Array GERDA experiment, located at the Laboratori Nazionali del Gran Sasso (LNGS) of INFN, searches for $0\nu\beta\beta$ of $^{76}$Ge. Germanium diodes enriched to $\sim 86~\%$ in the double beta emitter $^{76}$Ge ($^{enr}$Ge) are exposed being both source and detectors of $0\nu\beta\beta$ decay. Neutrinoless double beta decay is considered a powerful probe to address still open issues in the neutrino sector of the (beyond) Standard Model of particle Physics. Since 2013, just after the completion of the first part of its experimental program (Phase I), the GERDA setup has been upgraded to perform its next step in the $0\nu\beta\beta$ searches (Phase II). Phase II aims to reach a sensitivity to the $0\nu\beta\beta$ decay half-life larger than $10^{26}~$yr in about 3 years of physics data taking. This exposing a detector mass of about $35~$kg of $^{enr}$Ge and with a background index of about $10^{-3}~$cts/(keV$\cdot$kg$\cdot$yr). One of the main new implementations is the liquid argon scintillation light read-out, to veto those events that only partially deposit their energy both in Ge and in the surrounding LAr. In this paper the GERDA Phase II expected goals, the upgrade work and few selected features from the 2015 commissioning and 2016 calibration runs will be presented. The main Phase I achievements will be also reviewed.Comment: 6 pages, 12 figures, paper for the ICNPA 2016 conferenc

Necessary and sufficient conditions for robust gain scheduling

Recent results in the design of controllers for parameter dependent systems are extended to systems with plant uncertainty. The solution takes the form of an affine matrix inequality (AMI), which is both a necessary and sufficient condition for the posed problem to have a solution. The results in this paper may be used for the design of gain scheduled controllers for a class of uncertain systems

LMI approach to mixed performance objective controllers: application to Robust ℋ2 Synthesis

The problem of synthesizing a controller for plants subject to arbitrary, finite energy disturbances and white noise disturbances via Linear Matrix Inequalities (LMIs) is presented. This is achieved by considering white noise disturbances as belonging to a constrained set in ℓ2. In the case of where only white noise disturbances are present, the procedure reduces to standard ℋ2 synthesis. When arbitrary, finite energy disturbances are also present, the procedure may be used to synthesize general mixed performance objective controllers, and for certain cases, Robust ℋ2 controllers

Neutrinoless Double Beta Decay Search with 76^{76}Ge: Status and Prospect with LEGEND

The search for neutrinoless double beta ($0\nu\beta\beta$) decay is the best way to test lepton number violation and Majorana nature of neutrinos. One of the most promising techniques to discover $0\nu\beta\beta$ decay is by operating High-Purity Ge detectors enriched in $^{76}$Ge. The current generation of $^{76}$Ge experiments, GERDA and MAJORANA, lead the field in the achieved energy resolution and ultra-low background. These are two of the most important characteristics for sensitive searches of this undiscovered decay. The next generation of $0\nu\beta\beta$ decay experiments requires more mass and further reduction of backgrounds to maximize the discovery potential. Building on the successes of GERDA and MAJORANA, the LEGEND collaboration has been formed to pursue a tonne-scale $^{76}$Ge experiment, with a discovery potential projected to be a half-life beyond 10^{28} years. The collaboration aims to develop a phased experimental program, starting with a 200 kg measurement by repurposing the existing Gerda infrastructure.Comment: Contribution to the 2019 EW session of the 54th Rencontres de Moriond, 6 pages, 7 figure

The Cayley-Menger determinant is irreducible for n≥3n\geq 3

We prove that the Cayley-Menger determinant of an $n$-dimensional simplex is an absolutely irreducible polynomial for $n\geq3.$ We also study the irreducibility of polynomials associated to related geometric constructions.Comment: 7 pages, 4 figure