This paper proposes a closed form solution to
L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can express the
L2-sensitivity by a simple linear combination of exponential functions and formulate the
L2-sensitivity minimization problem by a simple polynomial equation. As a result, the
L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.
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