On the Design Approach of Robust Sliding mode Observers by Using LMI

This paper discusses the designing approach of the sliding mode observers. Based on Edwards's sliding mode observer, a robust sliding mode observer is presented, and the singular value decomposition technology endows the canonical process with simplicity. Then the linear feedback gain and the nonlinear feedback gain of the robust sliding mode observer are synthetically processed by Linear Matrix Inequalities (LMIs), and the nonlinear discontinuous injection is designed to modulate the convergence rate between the observer and the system, so as to attain the desired performances of the state estimation. At last, a numerical example is presented to illustrate the proposed method.