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In this work we study the stability of digital controls of flexible/Vibratory aerospace/automobile systems by the graph norm technique, occurring in sampled-data control systems due to sampling period variations. To do so, this work tries to establish regions (graphs) of stability and instability in a Banach Space, the distances (norms) between them and a given design to detect analytically and/or numerically its margins of stability or conditions of instability. Based on that, we sketch the first steps for a design methodology of stable digital controllers of flexible/vibratory systems embedded in a sampled-data system with adjustable sampling periods of A/D and D/A converters. A short tutorial about the graph norm technique is also given and some theoretical results as well numerical results are shown. This work was done in two folds to unmask the stability secrets hidden in a general sampled-data control system, until today not revelated. The first part we have used the graph norm and at the second part we made use of the Liapunov stability theory. PART I: TRIALS THROUGH THE NORM GRAPH TO OBTAIN SOME INFORMATION ABOUT STABILITY REGIONS FOR SAMPLED CONTROL SYSTEMS AS FUNCTION OF THE SAMPLING PERIOD As explained in [1], the true discrete could be given by ∑ ∞ −∞ = ≠π − ω = − − + =

Stability of Digital Controls of Flexible/Vibratory Aerospace/Automobile Systems by the Graph Norm