Robustness analysis of LTI systems with structured incrementally sector bounded nonlinearities

This paper addresses the stability analysis of a negative feedback interconnection of a multivariable linear time-invariant system and a structured time-invariant incrementally sector bounded nonlinearity. The classic Zames-Falb multiplier (1968) is extended to the multivariable case and is approximated arbitrarily closely by linear matrix inequalities. The problem of finding the multiplier that provides the largest stability bound then becomes a convex optimization problem over state space parameters. The method is also applied to symmetric incrementally sector bounded structured nonlinearities and provides an upper bound for the generalized structured singular value. Numerical examples are provided to demonstrate the effectiveness of this method.