Abstract: In order to further analyze and design the control system, the dynamic output feedback controller is designed for discrete time-delay singularly perturbed uncertain control systems to make the closed-loop system asymptotically stable. A new quadratic summation type L-K function is constructed for both delay dependent and delay independent case. The functional difference process is amplified by cross-term defined method, and the uncertainty of the system is eliminated by using the appropriate lemmas, the sufficiently existent criterion of dynamic output feedback controller with time delay is derived to expand the perturbation control range of the controller. The effectiveness and feasibility of the proposed method are verified by the showed example. Based on comparing the corresponding literature, it is shown that the proposed controller has certain advantages and makes the closed-loop system asymptotically stable. It meets the design requirements, and can achieve the secondary control effect.

Key words: output feedback control law, discrete uncertain systems, Schur complement lemma, Lyapunov-Krasovskii functional, linear matrix inequality (LMI), cross terms defined method