Interval Impulsive Observer for Linear Systems With Aperiodic Discrete Measurements
Djahid Rabehi, Nacim Meslem, Adnen El Amraoui, Nacim Ramdani
Abstract
This article addresses the modeling and the design of an interval state observer for a linear time-invariant plant in the presence of sporadically available measurements corrupted by unknown-but-bounded errors and noise. The interval observer is modeled as an impulsive system where an impulsive correction is made whenever a measurement is available. The non-negativity of the observation error between two successive measurements is preserved by applying the internal positivity based on the Müller's existence theorem, while at measurement times a linear programming constraint is added. A new methodology for designing the discrete-time observer gain is proposed that guarantees both nonnegativity and stability of the estimation error. The synthesis is performed by solving a set of bilinear matrix inequalities (BMIs). The theoretical result is supported by numerical simulation.