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H∞ Filtering for Singular Bilinear Systems with Application to a Single-link Flexible-joint Robot
Harouna Souley Ali,Mohamed Zerrougui,Mohamed Darouach,Latifa Boutat-Baddas 제어·로봇·시스템학회 2014 International Journal of Control, Automation, and Vol.12 No.3
In this paper, we consider the H∞ filters design for singular bilinear systems. The approach is based on the parameterized solution of a set of constrained Sylvester equations. The exponential convergence and l2 gain attenuation problems are solved by using the bounded real lemma, which leads to linear matrix inequalities (LMI) formulation. Finally, a detailed design procedure is given for the estimation of the states of a flexible joint robot, which demonstrates the effectiveness of the proposed method.
Full Order H_∞ Filtering for Linear Systems in the Frequency Domain
Montassar Ezzine,Harouna Souley Ali,Mohamed Darouach,Hassani Messaoud 제어·로봇·시스템학회 2011 International Journal of Control, Automation, and Vol.9 No.3
This paper proposes an easier frequency domain solution to the standard H_∞ filtering problem using a polynomial approach. The design of the H∞ filter in the frequency domain is first obtained from the time domain solution which is related to a Riccati equation, and then by the use of the connecting relationship between the time and frequency domain approach given by Hippe [8], its representation in the frequency domain is derived. The filter is easy to calculate as it requires the computation of a single gain and it is easily implementable also. A numerical example is given to illustrate the presented approach.
Filtering for Bilinear Systems with a Lipschitz Nonlinearity Using LPV Approach
Benjamin Gerard,Harouna Souley Ali,Michel Zasadzinski,Mohamed Darouach 제어·로봇·시스템학회 2012 International Journal of Control, Automation, and Vol.10 No.6
This paper deals with the H∞ filtering problem for a class of nonlinear systems. This class of nonlinear systems is composed of a bilinear part and of a lipschitzian one. The use of an unbiasedness condition for the bilinear part (called quasi unbiasedness condition) permits to parameterize the filter matrices through a single gain. Two LPV (Linear Parameter Varying) extensions of the bounded real lemma are used to solve the filtering problem. This approach reduces the conservatism inherent to the boundedness of the inputs. Then the filtering solution is expressed in terms of LMI (Linear Matrix Inequality) to be verified at the vertices of a polytope. A numerical example is finally given to illustrate our approach.