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Linear impulsive dynamic systems on time scales. (English) Zbl 1201.34144

The authors consider the nonhomegenous linear impulsive dynamic system

x Δ =A(t)x+h(t),t𝕋(timescale),tt k ,
x(t k + )=x(t k )+B k x(t k )+c k ,k=1,2,,

where B k are n×n real matrices, A is a matrix-valued, real, rd-continuous, regressive function, h is a vector real function, and {c k } is a vector real sequence. The points of impulses t k are assumed to be right-dense. The existence and uniqueness of solutions to the initial value problems involving homogeneous as well as nonhomogeneous system are discussed. Properties of the associated transition matrix are established. The authors also give some sufficient conditions for the stablility of the system.

34N05Dynamic equations on time scales or measure chains
34A37Differential equations with impulses
34A30Linear ODE and systems, general
34D20Stability of ODE