A new approach to design set-membership state estimators for discrete-time linear systems based on the observability matrix

Abstract

The paper introduces a method for synthesising set-valued state estimators for uncertain discrete-time linear systems. Based on the past values of the input and output of the system and on its observability matrix, a non-conservative numerical scheme is proposed to characterise at each time instant a tight enclosure of the actual state vector of the system. Interval analysis and consistency techniques are applied to design this guaranteed state estimator. In addition, the finite-time convergence of the width of the estimated state enclosures is shown. A comparison study, with some existing methods in the literature, throughout numerical examples is presented.

Keywords:

• Discrete-time linear systems
• uncertain systems
• bounded error context
• set-membership state estimator
• interval observers
• interval analysis

Disclosure statement

No potential conflict of interest was reported by the authors.