Stability analysis of systems with nonlinearities

Stability analysis of systems with nonlinearities is considered. Multipliers that describe the nonlinearities are used for the analysis. It is in particular shown how Popov multipliers can be combined with multipliers for slope restricted nonlinearities. The stability analysis can be approximated by a feasibility test for linear matrix inequalities. This requires that we choose a finite dimensional subspace for the set of multipliers. The choice of suitable subspace is discussed and an example is given where a duality argument gives a bound for the possible performance of the multiplier for slope restricted nonlinearities