H2H2 regulation performance limitations for SIMO linear time-invariant feedback control systems

In this paper, we investigate the regulation properties pertaining to single-input multiple-output (SIMO) linear time-invariant (LTI) systems, in which the objective function of regulated response is minimized jointly with the control effort. We provide analytical closed-form expressions of the best achievable H2H2 optimal regulation performances against impulsive disturbance inputs for unstable/non-minimum phase continuous-time and discrete-time systems. We also modify the latter results by means of the delta operator and show the continuity property, i.e., we show that the continuous-time solution can be completely recovered when the sampling period tends to zero in the delta domain solution. We then apply the results to a magnetic bearing system and discuss relations between the sensor selection and the best achievable H2H2 performances.