A Novel Equivalent Input Disturbance-Based Adaptive Sliding Mode Control for Singularly Perturbed Systems

This paper develops a novel equivalent input disturbance (EID)-based adaptive sliding mode control (SMC) method for singularly perturbed systems (SPSs). Firstly, the block diagonalization approach is introduced to decompose the full-order SPSs exactly, and slow and fast subsystems are obtained by solving the upper and lower triangular matrices individually. Secondly, an EID is constructed to estimate the unknown disturbances with the observer gain and error system convergence analyzed. Then, depending on the decoupled reduced-order system models, a Lyapunov equation-based solution is adopted to construct a composite sliding surface. Finally, combined with the EID estimation, an adaptive SMC law is proposed to compensate the adverse effect of disturbances and the reachability condition is proven. The presented control strategy is free of any priori disturbances information while the satisfactory system performance can be guaranteed. Simulation results on two examples illustrate its superiority over the existing methods.