Consider the system
X(n + 1) = 0.8X(n) + U (n) + V (n), n ≥ 0 Y (n) = X(n) + W (n), n ≥ 0,
where X(0) = 0 and the random variables V (n), W (n) are independent with
V (n) =D N(0, 0.2) and W (n) =D N(0, σ 2).
(a) Implement the control described in Theorem 14.2 for σ 2 = 0.1 and σ 2 = 0.4
and simulate the controlled system.
(b) Implement the limiting control with the limiting gain and the stationary Kalman
filter for σ 2 = 0.1 and σ 2 = 0.4. Simulate the system.
(c) Compare the systems with the time-varying and the limiting controls.

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