Adaptive control of linear periodic systems

This paper deals with the adaptive control of linear systems with periodically time-varying parameters (referred to as LTP systems) in discrete-time. While a large literature exists on the adaptive control of linear time-invariant (LTI) systems, practically very little is known regarding adaptation when the parameters vary periodically. This may be attributed to the fact that adaptive control can be attempted only after the properties of the corresponding deterministic systems (i.e systems with all parameter known) are well understood and design procedures are well established. In contrast to LTI systems, even though LTP systems have been studied for decades, their properties are not well understood and design procedures for stabilizing and controlling them are not straightforward. However, as discussed in this paper, there are compelling reasons for dealing with the adaptive control of such systems. In the following chapters, an attempt is made to answer several questions related to LTP systems, some of which are listed below: How much of adaptive control theory of LTI systems can be extended to the LTP case? What accounts for the difficulties encountered in such extensions? To what extent are the methods used in the two cases similar, and when are they different? Further, when they are different, what reasons can be attributed for the differences? Throughout the paper many comments are included to improve its readability.