Chattering Suppression Single Phase Variable Structure Controller for Mismatched Uncertain Interconnected Systems with Extended Perturbations

Abstract

In this study, a chattering suppression single phase variable structure controller (CSSPVSC) has proposed for mismatched uncertain interconnected systems via a Moore-Penrose Inverse approach. Key achievements of this paper include: 1) a global stability of the subsystems is guaranteed by dismissing the reaching phase in conventional variable structure control (CVSC); 2) a chattering phenomenon in control input is effectively reduced by using tanh function; 3) an external perturbations is extended to an unknown k -order function of the state variables. Firstly, a reduce-order observer (ROO) is designed to estimate the unmeasurable state variables of the subsystems. Secondly, a ROO-based CSSPVSC is synthesized to force trajectories of each subsystem to a switching surface from an instance time. Next, an asymptotic stability condition of the closed-loop system is ensured by employing the Lyapunov function together with the linear matrix inequality (LMI) theory. Finally, simulation results based on the MATLAB software are showed to demonstrate the proposed method effectiveness.