H∞ Loop Shaping for Mixed Continuous/discrete-time Time-varying and Periodic Systems

The loop shaping scheme is applied to H∞-control of time-varying and periodic systems. The solution is given in a unified mixed continuous/discrete-time compact form. This implies that pure continuous-time and discrete-time applications simply appear as two different interpretations of the given results. Among the applications are also hybrid systems with time-driven discrete events. For periodic continuous-time systems, a lifted (or discretised) system model is used to catch the behaviour during the period. The results can be considered as a generalisation of the Glover-McFarlane loop shaping procedure.