Prescribed‐time robust control of nonlinear time‐delay systems with known and unknown disturbance bound

Abstract

AbstractThis paper investigates the prescribed‐time robust control problem of a class of nonlinear time‐delay systems, and proposes some new prescribed‐time robust stabilization results. First, by applying the full decomposition method based on the delay term, the paper obtains an equivalent model of original system and promotes existing prescribed‐time stability criterion of delay‐free system to delay one. Based on these, when the bound of the disturbance is known, we design the corresponding prescribed‐time stabilization and robust stabilization controller. On the basis, we further give several robust stabilization results for the unknown disturbance by designing a new prescribed‐time controller. Finally, the study of two illustrative examples shows that the results obtained of the paper work well in the prescribed‐time robust stabilization the nonlinear delay systems. It is well worth pointing out that, different from existing infinite‐time and finite‐time asymptotical results of nonlinear delay system, the closed‐loop system under the prescribed‐time controller can reach the desired position within the specified time, and has stronger anti‐interference ability.