단일입력 불확실 비선형 시스템에 대한 Utkin 정리의 증명

A Poof of Utkin's Theorem for SI Uncertain Nonlinear Systems

In this note, a complete proof of Utkin's theorem is presented for SI(single input) uncertain nonlinear systems. The invariance theorem with respect to the two nonlinear transformation methods so called the two diagonalization methods is proved clearly, comparatively, and completely for SI uncertain nonlinear systems. With respect to the sliding surface and control input transformations, the equation of the sliding mode i.e., the sliding surface is invariant, which is proved completely. Through an illustrative example and simulation study, the usefulness of the main results is verified. By means of the two nonlinear transformation methods, the same results can be obtained.