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Question: using matlab...

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using matlab2. Consider the first order system x =x+u with initial condition x(0) 1. An optimal state feedback controller is to be designed such that u -kx, to minimize the performance index (a) Substitute u=-kx and solve the differential equation forx(t). For which values of kis the closed loop system stable? (b) Assume k is chosen such that the system is stable. Substitute your solution x(t and ukx(t) in the integrand and determine the value of the performance index in terms of k. For which value(s) of k is this performance index minimized? (c) Determine k using MATLABs lar0 function and compare with your result in part (b).

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