H-infinity Sampled-Data Synthesis and Related Numerical Issues

Abstract

In this paper we give a compact derivation of new formulae for the synthesis of H-infinity, sampled-data controllers for continuous-time, linear, time-invariant plants. The approach taken is via the established technique of continuous lifting, which isometrically maps the continuous-time, linear, periodically time-varying, sampled-data problem to a discrete-time, linear, time-invariant problem. A state-space realisation for the sampled-data equivalent, discrete-time, linear, time-invariant plant is derived by solving a set of two-point, boundary-value problems. The new formulae derived are significantly more simple than those previously published and accomodate a direct feedthrough term from the disturbance inputs to the controlled outputs of the original plant. It is also shown that the resultant formulae can be easily re-structured to give a numerically robust algorithm for calculating the state-space matrices.