This paper presents results that can be used to validate input-output transient performance for modular control systems. If bounds in the time-domain are specified for inputs of an LTI SISO system, the techniques in this paper can determine the minimum set containing all possible outputs. If both input and output bounds are given, they can determine whether these specifications are met. Network delay affecting the input of the system is also considered. Finally, this paper extends the techniques for MIMO systems. The results are derived using the theory of convex sets. Several examples are presented to illustrate the results and demonstrate their application.

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