H2 static output feedback stabilization of linear continuous-time systems with a dilated LMI approach

In this paper, new sufficient dilated LMI conditions for the H₂ static output feedback control problem of linear continuous-time systems are proposed. In order to reduce the conservatism existing in early standard LMI methods, auxiliary slack variables with structure are employed along with a similarity transformation. This result is also extended to linear systems with polytopic uncertainty. It is also shown, in this paper, that the proposed dilated LMI-based solution always encompasses the standard LMI-based one provided that a given parameter is properly selected. Numerical examples are given to illustrate the advantages of the proposed method when comparison is made with the classical standard methods.