Singular systems simultaneously capture the dynamics and algebraic constraints in many practical applications. Output feedback admissible control for singular systems through a delta operator method is considered in this article. Two novel admissibility conditions, derived for the singular delta operator system (SDOS) from a singular continuous system through sampling, can not only produce unified admissibility for both continuous and discrete singular systems but also practical procedures. To solve the problem of output feedback admissible control for the SDOS, an existence condition and design procedure is given for the determination of a physically realisable observer for the state estimation, and then a suitable state-feedback-like admissible controller design based on the observer is developed. All of the conditions presented are necessary and sufficient, involving strict linear matrix inequalities (LMI) with feasible solutions obtained with low computational costs. Numerical examples illustrate our approach.
