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

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