Robust $$\mathcal{H}_\infty$$ H ∞ Observer-based Stabilization of Linear Discrete-time Systems with Parameter Uncertainties

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 \(\mathcal{H}_\infty\) 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.