Análisis de la estabilidad de los sistemas lineales con saltos markovianos en tiempo continuo

• Mayta Guillermo, Jorge Enrique ^[1] ; Echegaray Castillo, William C. ^[1] ; Berrospi Zapana, Martin E. ^[1]
  1. [1] Universidad Nacional de Ingeniería

     Universidad Nacional de Ingeniería

     Perú

     
• Localización: Selecciones Matemáticas, ISSN-e 2411-1783, Vol. 7, Nº. 1, 2020 (Ejemplar dedicado a: January - July), págs. 183-191
• Idioma: español
• DOI: 10.17268/sel.mat.2020.01.18
• Títulos paralelos:
  • Analysis of the stability of linear systems with continuous Markovian jumps
• Enlaces
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• Resumen
  • español

    En este trabajo analizaremos la estabilidad de los sistemas lineales con saltos markovianos en tiempo continuo. En primer lugar, se impone que la cadena de Markov sea homogénea y el espacio de estado sea finito.Luego se presentan los tipos de estabilidad, por ejemplo, estabilidad cuadrática promedio, estabilidad estocástica, estabilidad exponencial. La estabilidad en la media cuadrática se analiza mediante la parte real de los autovalores de una cierta matriz. Finalmente, se presenta una ecuación del tipo Lyapunov.

  • English

    In this paper analyzed the stability of linear systems with continuous Markovian jumps. Firstly, the conditions for the Markov chain to be homogeneous and the state space is finite are imposed. Then the types of stability are presented, for example quadratic average stability, stochastic stability, exponential stability and almost certain stability. Stability in quadratic mean is analyzed by the real part of the eigenvalues of a certain matrix. Finally, an equation of Lyapunov is presented.

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