Structured Uncertainty Analysis of Robust Stability for Multidimensional Array Systems.

This paper considers one of the fundamental issues in design and analysis of sampled multidimensional systems—that of uncertainty modeling and robust stability analysis. Methods of structured uncertainty analysis (µ-analysis) are extended toward systems with dynamical and noncausal spatial coordinates. The stability is understood in a broad sense and includes decay (localization) of system response along the noncausal spatial coordinates. Robustness of dynamical stability and spatial localization of response and boundary effects are addressed in a unified way. The main technical condition enabling the technical results of the paper is that the feedback loop including a multidimensional plant and controller does not have a feed-through in the dynamical (time) coordinate sense. As an example, this paper applies the multidimensional structured uncertainly analysis to closed-loop control of a cross-directional paper machine process. The paper formulates multidimensional models of the process, its controller, and a structured uncertainty. The uncertainty corresponds to a combination of errors in the actuator mapping, the cross-directional response gain, and the response width. [ABSTRACT FROM AUTHOR]