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hw6.09 -  C = p-1 1 2-1 2-1-2 1 P 1 Find a minimal...

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ECE521 Linear Systems Fall 2009 Homework 5: Due November 19 Problem 1 : Consider a continuous system defined by A and B , A = 0 1 0 0 0 0 1 0 0 0 0 1 1 1 - 3 4 , B = 1 0 0 0 0 0 0 1 Find two different matrices K so the eigenvalues of A - BK are - 1 ± i and - 2 ± i . Problem 2 : Consider a discrete system defined by A and B A = 3 3 3 1 0 0 0 1 0 , 1 0 0 Find a state feedback K so x ( k + 1) = ( A - BK ) x ( k ) goes to zero in at most 3 steps. Problem 3 : Consider a contiuous system defined by the following matrices: A = - 3 3 4 - 3 4 - 5 - 6 4 - 3 3 4 - 3 2 - 3 - 4 2 , B = - 1 1 2 - 2 - 1 1 2 - 1 , C = parenleftbigg - 1 1 2 - 1 2 - 1 - 2 1 parenrightbigg 1. Find a minimal realization
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Unformatted text preview:  , C = p-1 1 2-1 2-1-2 1 P 1. Find a minimal realization 2. Let ( ˆ A, ˆ B, ˆ C ) be the realization you ²ound in (1). Using state ²eedback stabilize the system. 3. I² possible stabilize the system using the output ²eedback. Problem 4: Consider a continues LTI system ˙ x = p-1 0 0 0 P x ( t ) + p 2 2 P u ( t ) , y ( t ) = (-1 1) x ( t ) I² possible, design an observer (a tracking system) that has eigenvalues at-2 ,-4....
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