A modified two-steps LMI method to design observer-based controller for linear discrete-time systems with parameter uncertainties

Abstract : This note deals with the problem of observer-based stabilization for discrete-time linear systems with norm-bounded parameter uncertainties. Thanks to slack variable technique and the two-step method, an LMI-based approach is provided to compute simultaneously all the main decision variable of the observer-based controller problem. Our approach is inspired from the classical two-steps method introduced by Stankovic et al. and the modified two-steps method introduced by Zemouche et al.. Some comments are reserved to emphasize and clarify the difference between the different variants of the two-steps method.A numerical example is provided in order to illustrate how the new algorithm is less conservative than previous results in literature.
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Cherifa Bennani, Fazia Bedouhene, Ali Zemouche, Hamza Bibi, Abdel Aitouche. A modified two-steps LMI method to design observer-based controller for linear discrete-time systems with parameter uncertainties. 6th International Conference on Systems and Control, ICSC 2017, May 2017, Batna, Algeria. ⟨10.1109/icosc.2017.7958736 ⟩. ⟨hal-01567355⟩

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