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Summary: Set-Valued Observer Design for a Class of Uncertain
Linear Systems with Persistent Disturbance1
Hai Lin
Guisheng Zhai
Panos J. Antsaklis
Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
Faculty of Systems Engineering, Wakayama University, 930 Sakaedani, Wakayama 640-8510, Japan
Abstract
In this paper, a class of linear systems affected by both
parameter variations and additive disturbances is con-
sidered. The problem of designing a set-valued state
observer, which estimates a region containing the real
state for each time being, is investigated. The tech-
niques for designing the observer are based on posi-
tive invariant set theory. By constructing a set-induced
Lyapunov function, it is shown that the estimation er-
ror exponentially converges to a given compact set with
an assigned rate of convergence.
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