Synthesis of the minimum L2-sensitivity realizations of second-order digital filters without iterative calculations

This paper proposes synthesis of the minimum L₂-sensitivity realizations of second-order digital filters without iterative calculations. We restrict ourselves to second-order digital filters and consider three cases of second-order digital filters: complex conjugate poles, distinct real poles, and multiple real poles. 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, we achieve the L₂-sensitivity minimization without iterative calculations.