General Solution to Standard H∞Control Problems for a Class of Infinite-dimensional Systems

This paper considers H^∞-control of infinite-dimensional systems whose transfer functions are expressible as the cascade connection of a rational transfer matrix and a scalar (possibly irrational) inner function. This class of systems is very suitable for describing many control problems in practice, when weighting functions are rational and plants have at most finitely many unstable modes. We show that this problem can be reduced to two (matrix-valued) Riccati equations and additional rank conditions. Furthermore, the obtained controller structure is completely characterized by the inner function and controllers for the finite-dimensional part. A numerical example is given to illustrate the result.