Question: a. Consider the following state space model with fault definition. x = (A + AAF)x + (B + ABF)u + Eff y = (C

a. Consider the following state space model with fault definition. x = (A + AAF)x + (B + ABF)u + Eff y = (C + ACF)x + (D + ADF)u + Fff where = , ; = B0Bi; ACF = Ceci; and ADF = Die Di simplify the above equation for only additive actuator fault in the system. b. Derive the detectability condition for the additive actuator fault. C. Show that multiplicative fault A, is detectable if and only if C(SIA)A(SIA)B = 0 Note that the above proof is in the text, you are asked to expand the proof only.

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