Relating H₂ and H_∞ norm bounds for hybrid systems

Abstract

We relate the H∞ and H2 norms for a type of MIMO hybrid system, which includes sampled-data feedback control systems, were a continuous-time plant is controlled by a digital compensator with hold and sampler. First, we 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, we 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. We 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.