Robust stability of discrete time-delay uncertain singular systems

The robust stability property of linear discrete time-delay singular systems with structured parametric uncertainties is considered. Under the assumptions that the nominal time-delay singular systems are regular, causal and stable, necessary and sufficient conditions based on μ-analysis and guardian map theory are obtained to guarantee the properties by transforming the problem into checking the nonsingularity of a class of uncertain matrices. A tight bound is obtained in terms of μ for keeping the discrete time-delay singular systems regular, causal and stable. The results can be easily extended to deal with robust D-stability problem. Two examples are given to show the feasibility of the approach.