1. Gain margin for a linear quadratic regulator. Let K be the optimal state feedback gain for the LQR problem with system ˙ x = Ax + Bu, state cost matrix Q ≥ 0, and input cost matrix R > 0. You can assume that (A, B) is controllable and (Q, A) is observable. We consider the system ˙ x = Ax + Bu, u = αKx, where α > 0. If α = 1, this gives the LQR optimal… (More)

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