Consider the system
X(n + 1) = 0.8X(n) + U (n) + V (n), n â‰¥ 0 Y (n) = X(n) + W (n), n â‰¥ 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, Ïƒ 2).
(a) Implement the control described in Theorem 14.2 for Ïƒ 2 = 0.1 and Ïƒ 2 = 0.4
and simulate the controlled system.
(b) Implement the limiting control with the limiting gain and the stationary Kalman
filter for Ïƒ 2 = 0.1 and Ïƒ 2 = 0.4. Simulate the system.
(c) Compare the systems with the time-varying and the limiting controls.