Problem 1 3 only Explain the physical meaning of the follow

Explain the physical meaning of the following performance index j = 1/2 x^T (NT) Sx (NT) + 1/2 sigma^(N-1)_k=0 [exp(kT)(x^T (k)Qx(k)) + u^T(k)Ru(k)] Specify a constant output feedback matrix so that the given system x^.(t) = [-1 0 0 -4] x(t) + [0 1 1 0] u(t) y(t) = [0 1] x(t) will have a closed-loop eigenvalue at -10. Using state feedback to decouple the following system x bar.(t) = [1 1 0 0 1 0 0 0 1] x(t) + [0 1 1 0 1 0] u(t) y(t) = [1 1 -1 0 1 0] x(t)

Solution

(1) the given equation is output periodic feedback controller,a type of multirate output feed back is developed for hyperthermia system.

(3)