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

Development in mixed (i.e., real and complex) structured singular value theory and the associated multiplier-based analysis results have greatly reduced the conservatism in the the analysis of systems with mixed uncertainty. 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 test, LMI state space tests are developed. The results are then to delta-domain Popov-type multipliers and with a numerical example.