Robust regulation of stable systems in the H ∞-algebra

Abstract

In this paper, robust regulation of stable infinite-dimensional plants with transfer functions in the H ∞-algebra is considered. The reference and disturbance signals are allowed to have an infinite number of poles on the imaginary axis, which makes it possible to consider e.g. arbitrary periodic signals. A controller depending on a positive scalar ε and design parameters Kk is proposed. The design parameters are matrices over H ∞, and by the main result of the paper, if the design parameters satisfy a certain condition, the proposed controller is a robust regulator for sufficiently small values of ε. The only knowledge needed to verify this condition is the so-called -stability of the plant and values of the plant transfer function at the poles of the reference and disturbance signals. The analysis in this paper is in the frequency domain and it is based on the fractional representation approach.