Question: [2] Consider a continuous time system described by d x (t)] -6 10x(t) x (t) dt [x (1)] [-600x3 (t)] y(t)= [100]x(t) = -11

[2] Consider a continuous time system described by d x (t)] -6 10x(t) x (t) dt [x (1)] [-600x3 (t)] y(t)= [100]x(t) = -11 0 1 x(t) + 5 u(t) a. Design a state observer. b. What are the eigenvalues of the enlarged system consisting of the original system and the observer? Find the observer gain such that the eigenvalues of the enlarged system are at -1, -1, -1, -1, -2 and -3. Note that we can directly measure x (t); obtain the estimation error dynamics for x. What is the convergence speed?

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