Optimization of Multipliers for Nonlinear Input-Output Stability Tests

Classes multipliers that can be used for producing alternative stability tests involving positive-real and singular-value conditions have been neatly parameterized by Zames, Falb, Willems, and Safonov [1-3]. However, the issue of how to select optimal multipliers has remained unresolved until now. The present paper addresses this issue, describing how linear programming can be used to compute optimal multipliers for systems having a single incrementally conic nonlinearity f(x).