Relating H2 and H∞ norm bounds for hybrid systems

The authors relate the H_∞ and H₂ norms for a type of MIMO hybrid system, which includes sampled-data feedback control systems, where a continuous-time plant is controlled by a digital compensator with hold and sampler. First, the authors derive the H_∞ norm bounds for MIMO purely continuous and discrete-time systems given information concerning the location of the poles. The results are the same as those for the SISO case. Second, the authors describe upper bounds on both H₂ and H_∞ norms for hybrid systems, based on fundamental relations derived by two different approaches, namely the hybrid state space approach and the fast sampling and lifting approach. The authors also show the properties and interpretation of a residual appearing in the bounds and investigate the upper bound of the H₂ norm for a purely continuous-time system based on the result for the general hybrid case