Invariance principles for switched systems with restrictions

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe

Design and implementation of a bootrom in a Linux capable RISC-V processor

El moviment de codi obert promet revolucionar el món del maquinari igual que el programari ha revolucionat. Gràcies a l'arquitectura de conjunt d'instruccions o ISA (de l'anglès Instruction Set Architecture) RISC-V de codi obert, molts projectes s'estan obrint camí per oferir una alternativa a l'hermètic i privatiu món de l'arquitectura de computadors. En aquest context neix el projecte DRAC, les sigles del qual fan referència, de l'anglès, a Designing RISC-V-based Accelerators for next-generation Computers. Aquest projecte, liderat pel Barcelona Supercomputing Center (BSC), desenvolupa processadors i acceleradors basats en la tecnologia RISC-V, amb l'objectiu d'accelerar tasques de seguretat, medicina personalitzada i navegació autònoma. Aquesta tesi té com a propòsit dissenyar, implementar i verificar una bootrom pel SoC (de l'anglès System on Chip) de 64 bits DRAC 22 nm. Aquest SoC integra un processador RISC-V de 7 etapes anomenat Sargantana. El disseny del SoC, basat en l'anterior \textit{tape-out} anomenat PreDRAC, es divideix en dues parts. Una part conté tots els components orientats a l'ASIC; l'altra conté els elements orientats a la FPGA. Una de les raons principals d'aquesta divisió és que no existia una bootrom orientada a ASIC i, per tant, calia utilitzar la FPGA per arrencar el xip. Amb la integració de la bootrom desenvolupada en aquesta tesi, el SoC serà capaç d'arrencar per ell mateix, eliminant la part orientada a la FPGA del disseny del SoC.The open-source movement promises to revolutionize the hardware world just as it has revolutionized software. Thanks to the open-source RISC-V instruction set architecture (ISA), many projects are making their way to offer an alternative in the hermetic and proprietary world of computer architecture. The DRAC project, whose acronym refers to Designing RISC-V-based Accelerators for next-generation Computers, was created in this context. This project, led by the Barcelona Supercomputing Center (BSC), develops processors and accelerators based on RISC-V technology, and their purpose is to accelerate security tasks, personalized medicine and autonomous navigation. This thesis aims to design, implement and verify a bootrom for the 64-bit DRAC 22 nm System on Chip (SoC). This SoC integrates an in-order 7-stage RISC-V core called Sargantana. The SoC design, based on the previous tape-out PreDRAC, is divided into two parts. One part contains all the ASIC-oriented components; the other contains the FPGA-oriented components. One of the main reasons for this division is that there was no ASIC-oriented bootrom, and therefore, it was necessary to use the FPGA to boot the chip. With the integration of the bootrom developed in this thesis, the SoC will be able to boot by itself, eliminating the FPGA-oriented part of the SoC design

The conformal transformation's controversy: what are we missing?

An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's issue is then revealed: these transformations relate complementary geometrical pictures of a same physical reality, so that, the question about which is the physical conformal frame, does not arise. In addition, arguments are given which point out that, unless a clear statement of what is understood by "equivalence of frames" is made, the issue is a semantic one. For definiteness, an intuitively "natural" statement of conformal equivalence is given, which is associated with conformal invariance of the field equations. Under this particular reading, equivalence can take place only if the metric is defined up to a conformal equivalence class. A concrete example of a conformal-invariant theory of gravity is then explored. Since Brans-Dicke theory is not conformally invariant, then the Jordan's and Einstein's frames of the theory are not equivalent. Otherwise, in view of the alternative approach proposed here, these frames represent complementary geometrical descriptions of a same phenomenon. The different points of view existing in the literature are critically scrutinized on the light of the new arguments.Comment: 17 pages, no figures. version accepted by General Relativity and Gravitation journa

El fondo antiguo de la biblioteca

En este curso se presentan los diferentes aspectos que presenta los fondos antiguos que se conservan en las bibliotecas, como un aspecto del patrimonio cultural de las sociedades. Por tanto se analizan las diversas problemáticas que afectan a los diferentes objetos patrimoniales que se consideran integran ese fondo antiguo.Universidad Nacional Autónoma de Méxic