hw4.09 - ECE521 Linear Systems Fall 2009 Homework 4 Due...

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Unformatted text preview: ECE521 Linear Systems Fall 2009 Homework 4: Due Never These are some practice problems that may help your preparation for the upcoming midterm exam. Problem 1 : Consider the continuous system: ˙ x ( t ) = parenleftbigg 1 0 2 3 parenrightbigg x ( t ) + parenleftbigg 1 2 parenrightbigg u ( t ) y ( t ) = [ c 1 c 2 ] x ( t ) Under what conditions on [ c 1 c 2 ] is the system observable? Problem 2 : Consider the continuous system: ˙ x ( t ) =   0 1- 1- 2 0- 1 0   x ( t ) +   1 1   u ( t ) y ( t ) = [1 1- 1] x ( t ) • Find bases for the reachable but unobservable subspaces for the system. Problem 3 : Consider the discrete system x k +1 =   1 0- 1 0 1 1 0- 1   x k +   1 1   u k x = 0 If it is possible, calculate u k which takes the system form rest (that is from state x = [0 0 0] T ) to the state x f = [3 6 2] T . Problem 4 : 2 Suppose that x ( t ) = Ax ( t ), t ∈ R , and that A ∈ R 3 × 3 is a constant. Say we have found three expressions for state...
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hw4.09 - ECE521 Linear Systems Fall 2009 Homework 4 Due...

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