We consider hybrid difference-differential systems and analyze statements of initial-boundary value problems for such systems as compared with systems with retarded argument of the neutral type. We study the stability of solutions of linear stationary hybrid difference-differential systems and derive necessary and sufficient conditions for their asymptotic and exponential stability. In the scalar case, these conditions are refined and expressed via the original coefficients of the system in parametric form, which permits one to keep track of how the perturbations in the coefficients affect the solutions and to find the limiting value of the delay for which stability is preserved. [PUBLICATION ABSTRACT]
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