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hmwk3

# hmwk3 - University of California Santa Barbara Department...

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University of California, Santa Barbara Department of Electrical & Computer Engineering ECE 147b: Digital Control Winter 2009 Homework 3. Due 5.00pm Friday, 20th February, 2009 in the homework boxes on the 3rd. floor of Harold Frank Hall. If you use Matlab to solve any part of the homework, you must attach a copy of the Matlab script to your homework to get any credit for the problem. Problem 1. Consider two discrete-time state-space systems, P 1 ( z ) = bracketleftbigg A 1 B 1 C 1 D 1 bracketrightbigg , and P 2 ( z ) = bracketleftbigg A 2 B 2 C 2 D 2 bracketrightbigg . Each of these systems has more than one input and output. The number of poles in P 1 ( z ) is n 1 and the number of poles in P 2 ( z ) is n 2 . Calculate a state-space realization for each of the following interconnections. The “ A ” matrix of your realization must not have dimension greater than n 1 + n 2 . a) P 1 ( z ) + P 2 ( z ). Also sketch this as a block diagram with two blocks ( P 1 ( z ) and P 2 ( z )). What are the relationships between the numbers of inputs and outputs of P 1 ( z ) and P

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hmwk3 - University of California Santa Barbara Department...

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