Exponentially Stable Sliding Mode Based Approach for a Class of Uncertain Multi-Time-Delay Systems

This paper presents an adaptive fuzzy sliding mode control for a class of uncertain nonlinear systems with multiple time delays. The proposed control scheme guarantees to achieve an exponentially stable sliding surface even if mismatched uncertainty and unknown delays are considered. Compared to traditional schemes, the stability analysis is transformed into an LMI problem independent of each delay but a known upper bound of delay. Note that the uncertain dynamics is not canonical form. However, the novel sliding surface design can be derived based on the Lyapunov-Krasovskii method. Then, an SMC-based adaptive fuzzy control scheme is proposed to achieve asymptotic stability. Combined with the adaptive fuzzy algorithm, the chattering phenomenon will be reduced effectively. Moreover, the fuzzy membership functions are tuned on-line. The advantages of the proposed controller are to drive the states to converge to zero asymptotically and to alleviate the chattering phenomenon when the states are around zero.