Robust admissibility analysis and synthesis of uncertain singular systems via delta operator approach

This paper investigates the problems of robust admissibility analysis and robust admissible control for uncertain singular systems through delta operator method. Firstly, a necessary and sufficient LMI-based condition is derived guaranteeing the admissibility of a linear singular delta operator system. Then, based on the above result, a necessary and sufficient LMI-based condition is obtained for the robust admissibility of an uncertain singular delta operator system. Furthermore, the existence condition and explicit expression of a state feedback robust admissible controller is also given in terms of matrix inequalities. Finally, a numerical example is presented to demonstrate the results in this paper.