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Robust H∞ Observer-based Stabilization of Linear Discrete-time Systems with Parameter Uncertainties

Cherifa Bennani, Fazia Bedouhene*, Hamza Bibi, Ali Zemouche, Rajesh Rajamani, Khadidja Chaib-Draa, and Abdel Aitouche
International Journal of Control, Automation, and Systems, vol. 17, no. 9, pp.2261-2273, 2019

Abstract : "This paper addresses the problem of observer-based stabilization of discrete-time linear systems in presence of parameter uncertainties and ℓ2-bounded disturbances. We propose a new variant of the classical two-step LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from stabilization by a static state feedback. In the second step, a part of the slack variable obtained is incorporated in the H∞ observer-based stabilization problem, to calculate simultaneously the Lyapunov matrix and the observer-based controller gains. The effectiveness of the proposed design methodology is demonstrated using the dynamic model of a quadruple-tank flow process system. Additional numerical illustrations are presented to show the superiority of the proposed Modified Two-Step Method (MTSM) from a LMI feasibility point of view."

Keyword : Bilinear matrix inequality (BMI), H∞ criterion, linear matrix inequalities (LMIs), observer-based control, uncertain systems.

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