hw6 - interval[0,T This corresponds to a ﬁnite-horizon...

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ME254/ECE217C, HW 6 Winter 2009 Due Thursday March 12 at 5pm in the box outside my oﬃce 1. Exercise 1 on page 49 of notes. 2. Consider the stable ﬁrst order, input-output LTI system ˙ x = - x + u y = x (a) Compute the H norm using the frequency domain formula. (b) Compute the L 2 [0 ,T ]-induced norm as a function of T , and plot it. Note that the H norm is the L 2 [0 , ) norm, so the limit of this function as T → ∞ should equal to the answer in the ﬁrst part. Note: The L 2 [0 ,T ] -induced norm is the system norm for inputs and outputs over the
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Unformatted text preview: interval [0 ,T ] . This corresponds to a ﬁnite-horizon LQP as done in class and the notes. The condition k G k L 2 [0 ,T ]-induced < γ is equivalent to the existence of a solution to a scalar diﬀerential Ricatti equation over the interval [0 ,T ] . Such scalar equations are analytically solvable (e.g. see wikipedia entry or use your solution to problem 1 above) 3. TBA 1...
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This note was uploaded on 03/23/2009 for the course ME 254 taught by Professor Bamieh during the Winter '09 term at UCSB.

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