hw5.09 - ECE521 Linear Systems Fall 2009 Homework 5: Due...

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Unformatted text preview: ECE521 Linear Systems Fall 2009 Homework 5: Due November 5 Problem 1: Consider the system ˙ x = parenleftbigg- 3 5- 3 parenrightbigg x + parenleftbigg 1 parenrightbigg · 1 bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright u x (0) = parenleftbigg 1 parenrightbigg y = [1 2] · x 1. Find the transfer function G ( s ). 2. We know that y ( t ) = Ce tA x (0) + integraldisplay t Ce A ( t- τ ) Bu ( τ ) dτ bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright y (0) ( t ) Using Laplace transform, find the output y (0) ( t ) when the initial state is zero. (Use Laplace transform tables). 3. Having computed y (0) ( t ) find y ( t ). Problem 2: Consider a single input single output (SISO) system ( ˆ A, ˆ B ) which is in canonical form, that is ˆ A = 1 . . . 1- q- q 1 · · · - q n- 1 , ˆ B = . . . 1 , ˆ C T = c c 1 ....
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hw5.09 - ECE521 Linear Systems Fall 2009 Homework 5: Due...

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