Bounded state reconstruction error for LPV systems with estimated parameters

The note deals with the state reconstruction of a class of discrete-time systems with time-varying parameters. While usually, the parameters are assumed to be online available and exactly known, the special and realistic situation when the parameters are known with a finite accuracy is considered. The main objective of the note is to show that, despite of the resulting mismatch between the true system and the model, the state reconstruction error boundedness can be guaranteed and an explicit bound can be derived. The proof is based upon the concept of input-to-state stability.