Observer-based single-phase robustness variable structure controller for uncertain interconnected systems without reaching phase

This paper proposes a decentralized single phase robustness variable structure controller (SPRVSC) for complex uncertain interconnected systems satisfying mismatching condition. A key achievement of this study is to eliminate reaching phase in variable structure control theory. A switching surface is specifically designed such that a robust performance against extraneous perturbations is accurately assured from the initial time of the motion. A reduced order estimator (ROE) with lowerdimensional systems is designed to estimate the plant's state variables which are not measured. Based on the ROE and Moore-Penrose inverse technique, a decentralized SPRVSC is explored for uncertain systems with mismatched interconnections and unknown disturbances. Furthermore, a sufficient condition is derived by Lyapunov approach and linear matrix inequalities (LMI) technique for guaranteeing the robust stability of motion dynamics in sliding mode. Finally, a numerical example is also confirmed by MATLAB software for showing the effectiveness of the proposed method.