Abstract: In order to further design and analyze the discrete control system so that the new closed-loop system is asymptotically stable and meets the expected performance index, a static output feedback controller is designed for singularly perturbed uncertain control systems in the case of delay dependence and delay independence. And a new quadratic summation type L-K functional is constructed, the functional difference process is amplified by means of the cross-term defined method, and the uncertainty functionof the system is eliminated by lemmas, the sufficient criterion of the static output feedback controller with time delays is obtained, which enlarges the control range of the controller. The effectiveness and feasibility of the derived conclusions are verified by the selected example, and the controller is more superior in times comparing the corresponding literature.

Key words: Schur complement lemma, singularly perturbed system, time-delay system, linear matrix inequality(LMI), cross-term defined method