A Closed Form Solution to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters Subject to L2-Scaling Constraints

This paper proposes a closed form solution to L2-sensitivity minimization of 2nd-order statespace digital filters subject to L2-scaling constraints. The proposed solution reduces a constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. Furthermore, by restricting ourselves to the case of 2nd-order statespace digital filters, we can formulate the L2-sensitivity minimization problem via hyperbolic functions. As a result, we can express the L2-sensitivity in closed form, whose minimization subject to L2-scaling constraints is achieved without iterative calculations.