Question: Suppose the system i = Ax+bu has state x in R and a single input u and is controllable. A is 3 3 and

Suppose the system i = Ax+bu has state x in R and

Suppose the system i = Ax+bu has state x in R and a single input u and is controllable. A is 3 3 and b is 3 x 1. Let the characteristic polynomial of A be X + a21 + a + ao. What are the A' and b' matrices for the system if we change to a new basis {b, Ab, Ab}? Why do we need to assume that the system is controllable?

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