Continuous sliding mode control for uncertain linear time-invariant systems with matched and unmatched uncertainties using the Lyapunov-function integral sliding mode

Abstract

In this paper, a novel integral sliding mode (ISM) design was used to deal with the problem of unmatched uncertainty rejection in uncertain linear time-invariant (ULTI) systems. First, a new type of Lyapunov-function integral sliding mode (LFISM) with the ability to suppress unmatched uncertainty and disturbance was introduced. Despite the unmatched uncertainty, the system is robustly stable in ideal sliding mode or ultimate uniform bounded (UUB) stable in non-ideal sliding mode on the proposed LFISM surface. Then, the corresponding sliding mode control (SMC) control was designed based on the augmented system with the added integrator to ensure the reachability of the proposed LFISM, which led to a continuous sliding mode control (CSMC). The proposed method was applied to an academic case and an aircraft attitude control plant, and the comparison simulation results showed that the LFISM has better performance and rejection ability to the unmatched uncertainties.