Question: A system has the vector differential equation as given in Equation (11.42). We want both state variables to be used in the feedback so that

A system has the vector differential equation as given in Equation (11.42). We want both state variables to be used in the feedback so that u(t) = -ki{Xi - k2 x2. Also, we desire to have a natural frequency wn for this system equal to 2. Find a set of gains k1 and k2 in order to achieve an optimal system when J is given by Equation (11.63). Assume xT(0) = [1 O}.

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