Numerical Methods for Linear Quadratic and H∞ Control Problems

We discuss the numerical solution of linear quadratic optimal control problems and H∞ control problems. A standard approach for these problems leads to solving algebraic Riccati equations or to the computation of deflating subspaces of structured matrix pencils. New structure preserving methods for these problems have been developed recently. These are faster than the conventional used methods and give results of full possible accuracy. The new methods can also be used for Riccati equations with an associated Hamiltonian matrix that has eigenvalues on the imaginary axis.