Sampling Random Transfer Functions

Recently, considerable attention has been paid to the use of probabilistic algorithms for analysis and design of robust control systems. However, since these algorithms require the generation of random samples of the uncertain parameters, their application has been mostly limited to the case of parametric uncertainty. Notable exceptions to this limitation are the algorithm for generating FIR transfer functions in Lagoa et al. and the algorithm for generating random fixed order state space representations in Calafiore et al. In this paper, we provide the means for further extending the use of probabilistic algorithms for the case of dynamic causal uncertain parameters. More precisely, we exploit both time and frequency domain characterizations to develop efficient algorithms for generation of random samples of causal, linear time-invariant uncertain transfer functions. The usefulness of these tools will be illustrated by developing an algorithm for solving some multi-disk problems arising in the context of synthesizing robust controllers for systems subject to structured dynamic uncertainty.