A Note About the Stability of a String of LTI Systems
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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 £ p stable for every p≥1. Since the ∞-norm of a transfer function is the smallest of all its induced £ p norms, the result presented here enables one to obtain a tighter estimate of the geometric rate of attenuation of the states of sys-terns in the string.
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