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The problem under investigation is the design of an observer for non uniformly observable bilinear systems. The bilinear system can be separated into two subsystems: one is uniformly observable and the other is not. A high gain observer is designed for the “observable part” while an unbiased observer is synthesized for the “unobservable part”. The exponential stability of the observation error for...
This paper deals with the ℋ∞ reduced order unbiased filtering problems for a nominal bilinear system. After solving the unbiasedness condition with an algebraic framework, an LPV approach is used to reduce the conservatism inherent to the boundeness of the inputs and the ℋ∞ filtering. Then the reduced order filtering solution is expressed in terms of LMI to verify at the vertices of a polytope.
In this paper, we consider the H∞ observers design for singular bilinear systems. The approach is based on the parameterized solution of a set of constrained Sylvester equations. The results can be seen as the unification of the full order, the reduced order and minimal order observers design for singular bilinear systems. The parameters of these observers are obtained by solving an LMI.
This paper deals with the observer-based compensator design for bilinear systems. A saturated quadratic control law is used with two kinds of LPV observers. The closed loop stability is achieved using results on large scale systems.
This paper investigates both the H∞ and robust H∞ reduced order unbiased filtering problems for, respectively, a nominal bilinear system and a bilinear system affected by norm-bounded structured uncertainties in all the system matrices. First, an algebraic framework is used to solve the unbiasedness condition and second, a change of variable is introduced on the inputs of the system to reduce the...
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