H-infinity set-membership observer design for discrete-time LPV systems

ABSTRACT

This paper presents a new set-membership observer design method for discrete-time linear parameter varying systems. The real process is assumed to be perturbed by unknown but bounded disturbances. The proposed set-membership observer provides a deterministic state interval that is build as the sum of the estimated system states and its corresponding estimation errors bounds. The observer design process is based on the offline solution of a finite number of linear matrix inequalities conditions that provide both the observer parameters and the ellipsoidal robustly positive invariant (RPI) sets for the estimation error dynamics. The main feature of the proposed approach concerns the fact that these RPI sets are used to frame, at every time-instant, the estimation error in an explicit way. Another novelty concerns the fact that the approach includes uniformly distributed random disturbances which belongs to the family of bounded disturbances. The a posteriori steady-state covariance matrix of the estimation error dynamics, perturbed by such disturbances, is used during the observer synthesis providing small RPI sets. Two numerical examples illustrate the behaviour of such observer and its easy implementation.

Keywords:

• Set-membership state estimation
• state observers
• robustly positive invariant sets
• bounded-real lemma
• H-infinity synthesis
• linear parameter varying systems

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 These matrices are constant for facilitating the solution of the LMIs, as it is often proposed in the context of the $H_{\mathrm{\infty }}$ observer synthesis. Otherwise, they can be forced to be constant by including appropriate filters as it is proposed in Apkarian et al. (1995).