Invariant sets via LPV-embedding for Lure nonlinear systems with unmatched nonlinearities

Abstract

We derive sufficient conditions for the existence of invariant sets for Lure nonlinear systems where the nonlinearity is not matched with the control input. The sector bounded non-linearity is represented as a time-varying parameterised linear function with bounded parameter variations, and the invariant sets are computed by embedding the nonlinear system into a convex polytopic LPV system. We show that the ‘matching’ condition for the nonlinearity can be relaxed for the case when the matrices associated with the nonlinearity satisfy a special relation. An example of a flexible manipulator is provided to illustrate the results.