Modelagem e análise de sistemas lineares com saltos markovianos em duas escalas de tempo

• Autor(a) principal: Santos, Felipe Otávio dos
• Data de Publicação: 2020
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações do LNCC
• Texto Completo: https://tede.lncc.br/handle/tede/331
• topic: Sistemas estocásticos; Markov, Processos de; Sistemas lineares; CNPQ::CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO

This thesis addresses the mean stability analysis and the L1 and L∞ performances of continuous-time Markov Jump Linear Systems (MJLS) in which the abrupt changes are driven by a two-time-scale Markov chain, in the scenario in which the temporal scale parameter tends to zero. The jump process considered here is bivariate, with slow and fast components. Our approach relies on a convergence analysis involving the semigroup that generates the first-moment dynamics of the MJLS, when the switching frequency of the fast part of the Markov chain tends to infinity. In this setup, we introduce a new definition of stability in a limit case, and connect it with the mean stability of an averaged MJLS. In the particular case where the averaged MJLS is positive, we also derive suitable criteria for assessing mean stability and the L1 and L∞ performances with respect to deterministic disturbances. These criteria are expressed in terms of the spectral abscissa of a given matrix, of linear programming, and of the norms of a transfer matrix, which makes them suitable for computational purposes. We also establish comparisons between our (two-time-scale) approach and existing approaches from the literature, and show that our criteria are based on matrices of relatively smaller dimensions, which do not depend on the scale parameter . The effectiveness of the main results is discussed through numerical examples involving coupled electrical machines, epidemiological and compartmental models, and power allocation in telecommunications networks.