Characterize the effect of complementary gain conditions

Characterize the impact of the gain-condition regimes complementary to those analyzed for the discrete-time PI+Reset marginal-cost consensus controller and average power-mismatch estimator on the resulting system behavior, rather than relying on trial-and-error exploration.

Background

The paper analyzes how the controller gains affect the eigenvalue magnitudes of the discrete-time PI+Reset schemes under several sufficient stability conditions. The authors acknowledge that these conditions are somewhat conservative and do not determine how the unexamined complementary parameter regimes affect convergence or system performance.

Resolving this issue would provide a more complete characterization of admissible gain choices and could reduce reliance on empirical tuning when designing the marginal-cost consensus and average power-mismatch estimation controllers.