This paper proposes a closed form solution to L₂-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the 2nd order case of state-space digital filters, we can formulate L₂-sensitivity minimization problem by hyperbolic functions. As a result, L₂-sensitivity minimization problem can be converted into a problem to find the solution to a 4th degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations