Consider the metasystem (5.44) with A and B as given by (5.45) (a) Using the algebraic...

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Consider the metasystem (5.44) with A and B as given by (5.45) (a) Using the algebraic controllability test (5.23), show that the metasystem is not controllable. (This result is intuitively obvious.) (b) Assume that only the state x (and not xo) is measured, i.e., y = Cx, and that the original system x = Ax + Bu is observable (i.e., [C', A'C', ..., (A) C'] is of rank k). Discuss the conditions under which the metasystem is observable. Consider the metasystem (5.44) with A and B as given by (5.45) (a) Using the algebraic controllability test (5.23), show that the metasystem is not controllable. (This result is intuitively obvious.) (b) Assume that only the state x (and not xo) is measured, i.e., y = Cx, and that the original system x = Ax + Bu is observable (i.e., [C', A'C', ..., (A) C'] is of rank k). Discuss the conditions under which the metasystem is observable.

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a Controllability test The metasystem is not controllableThis can be shown using the algebraic controllability testwhich states that a system is contr... View the full answer