Robustness analysis in the delta-domain using fixed-structure multipliers

Developments in mixed (i.e., real and complex) structured singular value theory multiplier-based analysis results have greatly reduced the conservatism in the the analysis of systems with mixed uncertainty. However most of these advances have focused on continuous-time systems although. in practice it is more natural to;consider discrete-time systems. Hence, this paper presents robustness tests for the analysis of discrete-time systems. To avoid the inherent numerical ill-conditioning resulting from the use of the standard forward-shift representation and to help unify continuous-time and discrete-time robustness theories the developments are based on the delta-domain representation of a discrete-time system, After presenting a general frequency-domain robustness space tests are developed. The results are then specialized to delta-domain Popov-type multipliers and illustrated with a numerical example.