Adaptive Control Question

Dear Gentle Persons,
I am engage in MS research on using Observers for fault detection and Isolation on Non-linear systems in the presence of non-Gaussian Noise.
However, my question at the moment concerns an issue with Example 2.7 in the Book "Adaptive Control" by Astrom, Wittenmark. This example states that a single input of a generic periodic signal with period n can be at most a Persistant Excitation order of n.
I had a lot of trouble with this statement the first six times I read it, but I believe I may get it, but I would like make sure I get it right. The statement assumes that u(t) is discretly periodic with period n, thus you can have at most n different sample values, before they repeat.
What initially confused me was thinking of u(t) as a continous signal with period p close to, but not exactly equal to n. In this case you could in theory have inputs to the system that took on any value between the limits of u(t) that your system resolution would support.
So did I get the explanation right?
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Dear Gentle Persons,
I am engage in MS research on using Observers for fault detection and Isolation on Non-linear systems in the presence of non-Gaussian Noise. However, my question at the moment concerns an issue with Example 2.7 in the Book "Adaptive Control" by Astrom, Wittenmark. This example states that a single input of a generic periodic signal with period n can be at most a Persistant Excitation order of n.
I had a lot of trouble with this statement the first six times I read it, but I believe I may get it, but I would like make sure I get it right. The statement assumes that u(t) is discretly periodic with period n, thus you can have at most n different sample values, before they repeat.
What initially confused me was thinking of u(t) as a continous signal with period p close to, but not exactly equal to n. In this case you could in theory have inputs to the system that took on any value between the limits of u(t) that your system resolution would support.
So did I get the explanation right?
Add pictures here
<% if( /^image/.test(type) ){ %>
<% } %>
<%-name%>
Add image file
Upload

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