4. (20%) Consider LTI systems (A, B,C). (a) (10%) Show that (4, B) is controllable if and only if the state flow can be freely generated by open-loop control. (b) (10%) Let (4,C) be observable. Show that the value of the state at any time t, x(1), is able to be real-time determined by the control actions u(r), the measurement outputs y(t), re[1,1+8) for Ve > 0.
4. (20%) Consider LTI systems (A, B,C). (a) (10%) Show that (4, B) is controllable if and only if the state flow can be freely generated by open-loop control. (b) (10%) Let (4,C) be observable. Show that the value of the state at any time t, x(1), is able to be real-time determined by the control actions u(r), the measurement outputs y(t), re[1,1+8) for Ve > 0.
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Transcribed Image Text:4. (20%) Consider LTI systems (4, B,C).
(a) (10%) Show that (4, B) is controllable if and only if the state flow can be freely generated by
open-loop control.
(b) (10%) Let (4, C) be observable. Show that the value of the state at any time t, x(1), is able
to be real-time determined by the control actions u(r), the measurement outputs y(t),
rE[1,1+8) for Ve > 0.
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