 
Summary: Setvalued observer design for a class of uncertain linear systems with persistent disturbance and
measurement noise
HAI LINy*, GUISHENG ZHAIz and PANOS J. ANTSAKLISy
In this paper, a class of linear systems affected by parameter variations, additive noise and persistent disturbances is
considered. The problem of designing a setvalued state observer, which estimates a region containing the real state for
each time instant, is investigated. The techniques for designing the observer are based on positive invariant set theory. By
constructing a setinduced Lyapunov function, it is shown that the estimation error converges exponentially to a given
compact set with an assigned rate of convergence.
1. Introduction
In control theory and engineering, it is often desir
able to obtain full state information for control or diag
nostic purpose. Therefore it is not surprising that the
synthesis of a state observer has been of considerable
interest in classical system theory (see, e.g. O'Reilly
1983 and the references therein). The original theory
of state observer involves the asymptotic reconstruction
of the state by using exact knowledge of inputs and out
puts (Luenberger 1966). However, the real processes are
often affected by disturbances and noise. Therefore, the
design procedures of state observers were later extended
