Stability Analysis for a String of Coupled Stable Subsystems With Negative Imaginary Frequency Response

For a string of (possibly arbitrarily many) coupled stable subsystems that are equipped with a dynamic property of negative imaginary frequency response, we characterize stability of the string by a dc gain condition that can be expressed as a continued fraction with verifiable convergence properties. Through analysis of the convergence of the continued fraction, we establish stability results for the string with various coupling gains and patterns. The derived results are applied to locally decentralized control of large vehicle platoons, possibly with heterogenous neighboring coupling.