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We study a class of matrices with a rank-1 interconnection structure, andderive a simple necessary and sufficient condition for diagonal stability. Theunderlying Lyapunov function is used to provide sufficient conditions fordiagonal stability of approximately rank-1 interconnections. The main result isthen leveraged as a key step in a larger stability analysis problem arising inpower systems control. Specifically, we provide the first theoretical stabilityanalysis of automatic generation control (AGC) in an interconnected nonlinearpower system. Our analysis is based on singular perturbation theory, andprovides theoretical justification for the conventional wisdom that AGC isstabilizing under the typical time-scales of operation. We illustrate how ourmain analysis results can be leveraged to provide further insight into thetuning and dynamic performance of AGC.

Diagonal Stability of Systems with Rank-1 Interconnections and Application to Automatic Generation Control in Power Systems