This note concerns the stability of a string of LTI systems; it is shown here that, if the “weak interaction” condition among systems in the string is satisfied (i.e., the sum of the ∞-norms of the interaction/error propagation transfer functions is less than unity), then the string is Lp stable for every p⩾1. Since the ∞-norm of a transfer function is the smallest of all its induced Lp norms, the result presented here enables one to obtain a tighter estimate of the geometric rate of attenuation of the states of systems in the string.

Issue Section:
Technical Briefs
Keywords:
linear systems, transfer functions, stability criteria
Topics:
Stability, String, Transfer functions, Errors
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 by ASME
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