A revised computational procedure for calculating Zames-Falb multipliers

UnrestrictedThe search for Zames-Falb multipliers is a method by which the stability of a system with a monotone nonlinear feedback can be determined. An initial algorithm for computing these multipliers proposed by Safonov and Wyetzner uses a large set of basis elements and is thus computationally intensive. Later, Gapski and Geromel proposed a new algorithm which treats the problem as an optimization problem and uses a small set of basis elements. However, it is found that occasionally their algorithm terminates prematurely and fails to find the optimal multiplier. This thesis proposes an improvement that always finds an ascent direction and a multiplier that improves the cost function whenever one exists. Application of the new procedure for calculating Zames-Falb multipliers is further extended from the case of a basis set comprised of impulses to the generalized basis set proposed by Chen and Wen comprised of decaying exponentials