| Title |
A Poof of Utkin's Theorem for SI Uncertain Nonlinear Systems |
| DOI |
https://doi.org/10.5370/KIEE.2017.66.11.1612 |
| Keywords |
Variable structure system ; Sliding mode control ; Proof of Ukin's Theorem ; Diagonalization methods ; Transformation methods |
| Abstract |
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. |