Abstract
The control and command of singular systems of non-regular type pose very complex problems for automation engineers. The classic concepts of controllability are not applicable because of the non-regularity of the response of such systems whose internal states are no longer controllable in the temporal or frequency plane. New concepts are rather considered such as R-Controllability and Imp-Controllability combined with [Formula: see text] type stabilization approaches. This paper proposes a new synthesis of a [Formula: see text] controller, written in terms of LMI-like matrix inequalities, dedicated to this type of system. The simulation results, of the controller synthesized on methanation plant are encouraging and have led to better performance compared to other scientific publications in the field.