Problem 7. (15 pts) The following system is given 3 [1] 0 0 · = 0 + 0 u, 2 -1 y = [o 1 0] x. = 0 - 2 A [1 It is known th

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Problem 7 15 Pts The Following System Is Given 3 1 0 0 0 0 U 2 1 Y O 1 0 X 0 2 A 1 It Is Known Th 1 (288.22 KiB) Viewed 31 times

Problem 7. (15 pts) The following system is given 3 [1] 0 0 · = 0 + 0 u, 2 -1 y = [o 1 0] x. = 0 - 2 A [1 It is known that A= 0 0 0 0 07 -2 0 0 2 -4 1 1 0 4 T T-1 (a) For each of the three modes of the system, determine its controllability and observability. (b) Suppose u(t) = 0. Find all possible x(0) such that x(t) + 0 as t+. (c) Suppose u(t) = 0. Find all possible x(0) such that y(t) + 0 as t +00. (d) Suppose x(0) = 0. Does there exist a bounded control input u(t) for which the corresponding state solution x(t) is unbounded? Explain why. (e) Suppose x(0) = 0. Does there exist a bounded control input u(t) for which the corresponding output y(t) is unbounded? Explain why. = =