Physics · Control Systems
What is the state-transition matrix Φ(t) of the system described by the state equation [x1', x2']T = [[0, 1], [-2, -3]] [x1, x2]T?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Φ(t) = [[2e-t-2e-2t, 2e-t-e-2t], [-2e-t+2e-2t, -2e-t+2e-2t]]
- 2Φ(t) = [[2e-t-e-2t, e-t-e-2t], [-e-t+e-2t, -e-t+2e-2t]]
- 3Φ(t) = [[2e-t-e-2t, e-t-e-2t], [-2e-t+2e-2t, -e-t+2e-2t]]✓
- 4Φ(t) = [[e-t-e-2t, e-t-e-2t], [-2e-t+2e-2t, -e-t+2e-2t]]
Correct answer
Φ(t) = [[2e-t-e-2t, e-t-e-2t], [-2e-t+2e-2t, -e-t+2e-2t]]
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