LQG control of linear lossless positive-real systems: the continuous-time and discrete-time cases

Lossless positive-real systems have been widely studied in the literature. They are systems in which the energy is entirely transferred between input and output. In this paper, new aspects related to the linear quadratic gaussian (LQG) control of lossless positive-real systems are reported including both the continuous-time and the discrete-time cases. Direct formulas for the calculation of the optimal gains will be introduced and the properties of the different structures of the LQG compensator obtained for the continuous-time and the discrete-time cases will be emphasized, also in view of designing positive-real LQG compensators. Numerical examples related to low-damped structures are also discussed to verify the possibility to design the LQG compensator on the basis of a lossless approximation.