Estabilidad de sistemas lineales impulsivos

Abstract

En este trabajo se estudia el problema de la estabilidad asintótica del sistema lineal impulsivo X' = AX, X(tk) = BX(t-k). Mediante ejemplos se muestra que la estabilidad asintótica de este sistema no proviene de la estabilidad asintótica del sistema diferencial ordinario X' = AX ni de la estabilidadasint6tica del sistema discreto X(k + 1) = BX(k). Se consigue un teorema de estabilidad asint6tica para el caso en que A y B son matrices triangulares.

In this work the problem of aymptotic stability of the impulsive system X' = AX,X(tk) = BX(t-k) is studied. By means of examples we show that the asymptotic stability of this system cannot be infered from the asymptotic stability of the linear differential system X' = AX, neither from the asymptotic stability of the discrete system X(k + 1) = BX(k). A theorem of asymptotic stability for the impulsive system X' = AX,X(tk) = BX((t-k), where A and Bare triangular matrices is obtained.