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Robust Stability: criterion for inverse multiplicative uncertainty
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[QUOTE="Master1022, post: 6439706, member: 650268"] [B]Homework Statement:[/B] Using the small gain theorem, derive the condition for multiplicative inverse uncertainty [B]Relevant Equations:[/B] Block diagram Hi, I have a question that I am quite confused about. Please note this is at the undergraduate level. [B]Question: [/B]Given the transfer function with inverse multiplicative uncertainty [tex] \bar G (s) = \frac{G(s)}{1+\Delta \cdot W(s) \cdot G(s)} [/tex] and the fact that the system is connected in feedback with controller [itex] K(s) [/itex], use the small gain theorem to derive the condition for the closed loop system to be stable: [tex] ||W(s) G(s) \cdot \frac{1}{1 + K(s)G(s)} ||_{\infty} < 1 [/tex] [B]Attempt:[/B] My problems are as follows: 1. I am not 100% confident about what the method is to do this 2. I am not sure how to draw this as a block diagram For q1, does the following method sound correct? - Draw the block diagram - Relate the output [itex] Y(s) [/itex] to the system [itex] G(s) [/itex], controller [itex] K(s) [/itex], and uncertainties (I am not quite sure how to properly do this step) - Then use the small gain theorem to get the above expression For q2, I have looked around on the internet, but the examples are ones where there isn't a [itex] G(s) [/itex] term in the denominator. I am especially confused about how to include an inverse in a block diagram. Does the following look like the correct start? [ATTACH type="full"]275614[/ATTACH] Thanks in advance for any help. [/QUOTE]
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Robust Stability: criterion for inverse multiplicative uncertainty
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