Robust $\mathcal{H}_{\infty}$ Observer-Based Stabilization of Linear Discrete-Time Systems with Parameter Uncertaintes

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-steps LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from the stabilization problem 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. Numerical evaluation by Monte Carlo is presented to show the superiority of the proposed Modified Two-Steps Method (MTSM) from LMI feasibility point of view.