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    Prove the Lyapunov equation

    The sufficiency can be obtained by considering B=\int_{0}^{∞} e^{A^τ t} Q e^{A t} dt Inserting into the Lyapunov equation gives AB + BA^{T} = A \int_{0}^{∞} e^{A^τ t} Q e^{A t} dt + \int_{0}^{∞} e^{A^τ t} Q e^{A t} dt A^{T} = \int_{0}^{∞} \frac{d}{dt} (e^{A^τ t} Q e^{A t}) dt = [e^{A^τ...
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