Reaching a Consensus in Networks of High-Order Integral Agents under Switching Directed Topology

Consensus problem of high-order integral multi-agent systems under switching directed topology is considered in this study. Depending on whether the agent's full state is available or not, two distributed protocols are proposed to ensure that states of all agents can be convergent to a same stationary value. In the proposed protocols, the gain vector associated with the agent's (estimated) state and the gain vector associated with the relative (estimated) states between agents are designed in a sophisticated way. By this particular design, the high-order integral multi-agent system can be transformed into a first-order integral multi-agent system. And the convergence of the transformed first-order integral agent's state indicates the convergence of the original high-order integral agent's state if and only if all roots of the polynomial, whose coefficients are the entries of the gain vector associated with the relative (estimated) states between agents, are in the open left-half complex plane. Therefore, many analysis techniques in the first-order integral multi-agent system can be directly borrowed to solve the problems in the high-order integral multi-agent system. Due to this property, it is proved that to reach a consensus, the switching directed topology of multi-agent system is only required to be "uniformly jointly quasi-strongly connected", which seems the mildest connectivity condition in the literature. In addition, the consensus problem of discrete-time high-order integral multi-agent systems is studied. The corresponding consensus protocol and performance analysis are presented. Finally, three simulation examples are provided to show the effectiveness of the proposed approach

El uso de Internet por parte de las personas mayores. Motivos y soluciones a la brecha digital en la ciudad de Valladolid

En la actualidad, la revolución de las nuevas tecnologías que representa Internet está reconstruyendo la estructura y las relaciones sociales. Cuando el envejecimiento se encuentra con la digitalización, cómo adaptarse y usar Internet es un tema importante y urgente para las personas mayores. Este artículo profundiza en el uso de Internet entre las personas mayores de Valladolid, centrándose en las actitudes y efectos de la tecnofobia, los factore económicos y la pandemia del COVID-19. Se realizó una triangulación de métodos, partiendo de una revisión bibliográfica del estado de la cuestión, en la que se basaron los cuestionarios empleados en las entrevistas a profesionales y expertos relevantes. Además, se realizó una encuesta a una muestra de conveniencia de 236 personas mayores en 12 centros de la ciudad. La investigación mostró que las razones técnicas no son determinantes en la decisión de las personas mayores de usar Internet, que no existe una correlación entre el costo económico y el uso de Internet, y que la pandemia de COVID-19 ha actuado como una fuerza impulsora para que las personas mayores vean necesidad de utilizar las TIC. Al mismo tiempo, el estudio encontró que el miedo a lo desconocido y la resistencia al cambio obstaculizaron en gran medida la aceptación de las TIC por parte de las personas mayores, lo que también proporcionó a los profesionales ideas para el trabajo futuro. Este estudio también argumenta que, en base a la motivación y el interés, se deben llevar a cabo campañas activas de sensibilización y capacitación para permitir que las personas mayores crucen la brecha digital y se integren mejor en el mundo digital.At present, the revolution of the new technologies that the Internet represents is rebuilding the structure and social relations. When aging meets digitization, how to adapt and use the Internet is an important and urgent issue for the elderly. This article delves into the use of the Internet among older people in Valladolid, focusing on the attitudes and effects of technophobia, economic factors, and the COVID-19 pandemic. A triangulation of methods was carried out, starting from a bibliographic review of the state of the art, on which the questionnaires used in the interviews with relevant professionals and experts were based. In addition, a convenience sample of 236 elderly people in 12 city centers was surveyed. The research showed that technical reasons do not influence older people's decision to use the Internet, that there is no correlation between the economic cost and the use of the Internet, and the COVID-19 pandemic has acted as a driving force for older people to see the need to use TIC. At the same time, the study found that fear of the unknown and resistance to change greatly hampered older people's acceptance of TIC, which also provided practitioners with ideas for future work. This study also argues that, based on motivation and interest, active awareness and training campaigns should be carried out to enable older people to cross the digital divide and better integrate into the digital world.Departamento de Historia Moderna, Contemporánea y de América, Periodismo y Comunicación Audiovisual y PublicidadMáster en Investigación de la Comunicación como Agente Histórico-Socia