Sampled-Data $H^{2}$ Optimization of Systems With I/O Delays via Analog Loop Shifting

The problem of sampled-data H² control of systems with a single input delay is studied. Conventional solutions of sampled-data optimal control problems begin with a conversion to a discrete-time problem with input delays, followed by a matching optimization method, geared to handle delays. We propose reversing that order and address the delay first, by an analog loop transformation. Hence, discretization and optimization involve no delays and are amenable to any standard method. The proposed, streamlined, approach fits also previously unsolved problems where sampling and/or hold functions are design parameters.