Numerical computation of H ∞ optimal performance

Abstract

We present new algorithms for computing the H ∞ optimal performance for a class of single-input/single-output (SISO) infinite-dimensional systems. The algorithms here only require use of one or two fast Fourier transforms (FFT) and Cholesky decompositions; hence the algorithms are particularly simple and easy to implement. Numerical examples show that the algorithms are stable and efficient and converge rapidly. The method has wide applications including to the H ∞ optimal control of distributed parameter systems. We illustrate the technique with applications to some delay problems and a partial differential equation (PDE) model. The algorithms we present are also an attractive approach to the solution of high-order finite-dimensional models for which use of state space methods would present computational difficulties.