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

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-step method introduced by Stankovic et al. and the modified two-step method introduced by Zemouche et al‥ Some comments are reserved to emphasize and clarify the difference between the different variants of the two-step method. A numerical example is provided in order to illustrate how the new algorithm is less conservative than previous results in literature.