b.) Is the system exponentially stable? Give a proof of your answer. c.) Is the system...

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b.) Is the system exponentially stable? Give a proof of your answer. c.) Is the system input-output stable (BIBO)? Question 5: A linear system has A (t) = -1 = 2 cos(2t) - 5 -1 1 2 cos(2t) - 5 a.) Use a quadratic Lyapunov function to determine the stability properties of this system. b.) Explicitly compute the state transition matrix for this system, and compare with your conclusions from a.) c.) Compute the P (t), Q and R components of the Floquet decomposition for this system and use these to assess the stability properties of the system. b.) Is the system exponentially stable? Give a proof of your answer. c.) Is the system input-output stable (BIBO)? Question 5: A linear system has A (t) = -1 = 2 cos(2t) - 5 -1 1 2 cos(2t) - 5 a.) Use a quadratic Lyapunov function to determine the stability properties of this system. b.) Explicitly compute the state transition matrix for this system, and compare with your conclusions from a.) c.) Compute the P (t), Q and R components of the Floquet decomposition for this system and use these to assess the stability properties of the system.