Sampled-data regulation of a class of time varying systems based on a realizable reconstruction filter

A sampled-data regulation problem for a class of continuous time varying systems is presented. The main constraint is the availability of only the samples of the output for measurement. The particular focus is on such linear time varying systems that can be transformed into linear time invariant systems through sinusoidal transformation. This converts the problem of tracking a constant signal into a sinusoidal signal. Typical to the sampled-data control problems, the control input is generated by a discrete controller along with a discrete observer for state and disturbance estimation. A realizable reconstruction filter, which is a reduced order specialized generalized hold device, connects the discrete controller with the continuous input of the system. The resultant linear time invariant system along with the realizable reconstruction filter is thus presented as a linear impulsive system. The rest of the problem is similar to the classical regulator theory. As an example the control of gyroscope in both perturbed and unperturbed scenarios is presented.