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

ABSTRACT–This paper proposes a closed form solu-tion to L2-sensitivity minimization of 2nd-order state-space digital filters subject to L2-scaling constraints. The proposed solution reduces a constrained optimiza-tion problem to an unconstrained optimization problem by appropriate variable transformation. Furthermore, by restricting ourselves to the case of 2nd-order state-space 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. 1.