Stochastic Periodic Systems

Abstract

In this chapter, we treat periodic systems subject to stochastic external actions. Systems of this type are useful not only to account for random effects but also to describe the uncertainties affecting the model at hand, as an imperfect, approximated description of part of the real world. As such, stochastic models represent a cornerstone in the developments of systems and control. In particular, a fundamental problem of our days, dynamic filtering, is effectively tackled starting from such models. Dynamic filtering is the problem of estimating the latent (state) variables of a system from the available measurement of (possibly few) observable signals. On-line filtering algorithms, Kalman filtering techniques in primis, have become a key ingredient in modern communication and control systems. The knowledge of the state supplied by the estimator is the basic information to decode a noisy signal or to decide the best action in a control chain.