Unified, periodic & sampled data H∞ control using the delta operator

A unified and general framework is presented for H_∞ control of mixed continuous-time and discrete-time time-varying (periodic) systems. Using the delta operator, a close relationship is shown between the continuous- and discrete-time solutions. No assumptions are made on certain system matrices being zero or normalized, which makes the approach general and easy to apply. A combined continuous/discrete-time lifting procedure is shown to be useful, especially for ill-conditioned systems. This procedure together with the delta formalism results in a numerically robust design method concerning both short and long sampling periods for systems with W-conditioned dynamics, including widely spread eigenvalues.