Figure 3

Stability analysis of feedback systems. (i) We decompose any given system as a feedback interconnection of a linear time-invariant system H and an otherwise system N. Stability of the feedback interconnection follows if there exists a hyperplane that separates the graph of H from the inverse graph of N. If N is a monotone nonlinearity, the Zames-Falb multipliers are commonly used to reduce conservatism in multiplier-based stability analysis of this system. (ii) The Nyquist plot of a Zames-Falb multiplier is constrained to lie inside an open disc in the right-half s-plane. (iii) Rantzer has investigated these distortions of monotone nonlinearities, and has shown that the stability multipliers for such systems can be obtained by adding a DC offset to the Zames-Falb multipliers (see [15]). The Nyquist plot of these multipliers is constrained to lie in the open disc shown in (iv).