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# Mid-Term Exam

ACCESS Mid-Term Exam (2011) All your answers have to be provided with solid arguments; you have to explicitly refer to results on the slides or the books! Show clearly how you have arrived at your results! Just giving results or answers (even if correct) will not be awarded with credits. Make sure to write down your student id-number on each page you hand in!

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Problem 1 (5+5=10 Points) The following algebraic and differential equations describe the depicted circuit: icily вЂ? 3 is PVC 1 + + 2 ERR vs. +- ICC dive EDT CLC dive where R = IQ and CLC = CA = IF . The capacitor voltages vs. and vs. can be regarded s the states of the system. A) Find the modes of the system and the corresponding mode-shapes based on a cetaceans description of the circuit. B) Find the responses of the system using the mode-shapes as the initial state vectors.

You need to calculate a response for each mode-shape. What can be concluded from the obtained responses? Problem 2 (7+5+3+5=20 points) Consider the following state-space system: 7 101 c a) Compute the Jordan form of A. B) Compute eat . C) Is it possible to drive the system from the initial state x(O) = final state described by x(TFH)= 105 oho to the ) Now consider the following system: 01 -1 4 x=010-1 OX+oho 11-2 100 Is this system equivalent to the former one?

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