Continuous-time input-output decoupling for sampled-data systems

The problem of obtaining a continuous-time (i.e., ripple-free) input-output decoupled control system for a continuous-time linear time-invariant plant , by means of a purely discrete-time compensator, is stated and solved in t he case of a unity feedback control system. Such a control system is hybrid , since the plant is continuous-time and the compensator is discrete-time. A necessary and sufficient condition for the existence of a solution of suc h a problem is given, which reduces the mentioned hybrid control problem to an equivalent purely continuous-time decoupling problem. A simple necessar y and sufficient condition for the existence of a solution of such a contin uous-time decoupling problem is given for square plants (with and without t he additional requirement of the asymptotic stability of the over-all contr ol system), together with a parameterisation of all the decoupling controll ers. Moreover, for square plants, it is shown that, whenever the hybrid con trol problem admits a solution, any solution of the corresponding decouplin g problem for the discrete-time model of the given continuous-time system i s also a solution of the hybrid control problem.