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 stable for every Since the ∞-norm of a transfer function is the smallest of all its induced 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.
A Note About the Stability of a String of LTI Systems
Contributed by the Dynamic Systems and Control Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS. Manuscript Received by the Dynamics Systems and Control Division January 1, 2000. Associate Editor: E. Fahrenthold.
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Darbha , S. (July 23, 2002). "A Note About the Stability of a String of LTI Systems ." ASME. J. Dyn. Sys., Meas., Control. September 2002; 124(3): 472–475. https://doi.org/10.1115/1.1485099
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