A modified two-stage LQ reliable control

This paper introduces a modified version of the previously proposed two-stage LQ reliable control (TSLQRC), which is a discrete-time version of Veillette´s reliable LQ regulator, such that the controls improve on the known performance gain margin results of the TSLQRC by tolerating the insertion of any independent gains into the whole feedback loops. It is shown that the desired gain margins satisfy a modified gain margin constraint. An application of the proposed modified gain margin constraint to design an optimal single-stage LQ reliable guaranteed cost controller is also illustrated. A numerical example is given to show the effectiveness of the proposed results.