Sensitivity of the stable discrete-time Lyapunov equation

The sensitivity of the stable discrete-time Lyapunov equation is analyzed through the spectral norm of the inverse Lyapunov operator. This leads to a directly computable easy-to-interpret sensitivity measure, which involves only the open-loop state matrix and also provides insight into the connection between sensitivity, stability radius, and conditioning of the eigenproblem of the open-loop state matrix. These results are an extension, to the discrete-time case, of analogous results for the continuous-time Lyapunov equation.<
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