Richness and excitation on an interval

An approach involving richness and excitation on an interval is used to address the excitation problem for time-varying systems which are almost time-invariant and unstable. The authors consider feedback laws which, when applied to any controllable time-invariant linear system, result in a closed-loop system such that the feedback signal, the measure of excitation which it produces, and the state vector of the system are all of the same order of magnitude on an interval. Such feedback laws generate excitation of time-varying linear systems, provided these systems are almost time-invariant and controllable in the interval of interest. In other words, if the input of a controllable, possibly unstable linear system is generated by rich feedback, then excitation on an interval carries over from the time-invariant to the slowly time-varying case