Descriptor formulation for a robust static output feedback $H_{\infty}$ control for polytopic discrete-time system

This paper investigates the problem of robust static output feedback (SOF)
$H_{\infty}$
controllers for polytopic uncertain discrete-time systems. The descriptor redundancy approach and linear matrix inequality (LMI) techniques are applied to solve the static output feedback
$H_{\infty}$
controllers problem. By considering auxiliary slack variables with free structure, new sufficient conditions for static output feedback
$H_{\infty}$
design are presented in terms of linear matrix inequalities (LMIs), which guarantee the robust stability of the closed-loop systems under prescribed
$H_{\infty}$
performances. Numerical ex-amples are given to illustrate the advantages of the proposed procedure when compared with other methods available in the literature.