Stability results for string of stable subsystems with applications to decentralized control of large vehicle platoons

We characterize the stability of a string of (possibly arbitrarily many) coupled stable subsystems 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 both stability and robustness for the string with various coupling gains and patterns. The derived stability results are used to achieve locally decentralized control of large vehicle platoons.