Chapter

Multiscale Optimization Methods and Applications

Volume 82 of the series Nonconvex Optimization and Its Applications pp 313-326

Shape Optimization of Transfer Functions

  • Jiawang NieAffiliated withDepartment of Mathematics, University of California
  • , James W. DemmelAffiliated withDepartment of Mathematics, University of California

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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.

Key words

Linear system transfer function shape optimization nonnegative polynomials convex cone semidefinite programming