Gain-Scheduled Observers Using Inexact Scheduling Parameters

This note addresses the design problem of Gain-Scheduled (GS) observers for discrete-time Linear Parameter-Varying (LPV) systems via Parameter-Dependent Lyapunov Functions (PDLFs). We give a sufficient condition for our problem in terms of Parameter-Dependent Linear Matrix Inequalities (PDLMIs). Our method not only guarantees the stability of estimation error dynamics but also optimizes the estimation errors under exogenous disturbances to LPV systems. A numerical example is included to illustrate our results.