$\mathcal{H}_{\infty}$ static output-feedback controllers with past outputs for discrete-time uncertain linear systems

This work investigates the problem of designing robust $\mathcal{H}_{\infty}$ static output-feedback controllers for uncertain linear discrete time-invariant systems where all matrices are supposed to be affected by polytopic uncertainties. The proposed control law employs a fixed number of past measured outputs, thus enhancing the dynamics of the closed-loop system and producing controllers with memory. The method for synthesizing the memory controllers relies on a two-phase algorithm. In the first phase a parameter-dependent state-feedback gain is designed and, then, it is used as input to the second phase in which the robust memory static output-feedback controller is synthesized. Numerical examples illustrate the advantages of the proposed approach in terms of $\mathcal{H}_{\infty}$ performance when compared to other methods available in the literature.