Observers and invariant sets for lure-type nonlinear systems using LPV-embedding

This paper deals with observers for Lure-type nonlinear systems designed so that the associated estimation error dynamics are bounded in an invariant set. The design uses the LPV-embedding technique, whereby the nonlinearity is redefined in terms of a time-varying parameterised linear function, called the `LPV parameter'. For LPV parameters with bounded variation, invariant sets for the original nonlinear system are computed by embedding the LPV system into a convex polytopic description. The trajectories of the estimation error are guaranteed to be bounded and remain in the computed invariant set, which exists if a condition in terms of the system matrices and parameters is satisfied. We show that arbitrarily small estimation error bounds can be achieved for some classes of systems. We illustrate the results via a simulation example of a flexible manipulator.