Question: Question 4. Problem 4 (20 points): Consider the following controlled continuous LTI system 561 = x1 + u(t) 32:2 = x2 + X3 5'3 =

Question 4.

Problem 4 (20 points): Consider the following controlled continuous LTI system 561 = x1 + u(t) 32:2 = x2 + X3 5'3 = 'xs 3' = x1 1. Initially, set u(t) = 0. Find all equilibrium points of the system. 2. Is the system controllable? Dene which modes are controllable and which modes are uncontrollable. 3. Is the system observable? Dene which modes are observable and which modes are not observable 4. Design, if possible, a feedback controller in the form u(x1,x2,x3) = ka = k1x1 kzxz k3x3 such that the output of the system behaves as y(t) = 3103'\" for any possible yo E R

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