Shape Optimization of Transfer Functions

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Summary

We show how to optimize the shape of the transfer function of a linear time invariant (LTI) single-input-single-output (SISO) system. Since any transfer function is rational, this can be formulated as an optimization problem for the coefficients of polynomials. After characterizing the cone of polynomials which are nonnegative on intervals, we formulate this problem using semidefinite programming (SDP), which can be solved efficiently. This work extends prior results for discrete LTI SISO systems to continuous LTI SISO systems.