| Title |
A Poof of Utkin's Theorem for a MI Uncertain Linear Case |
| Keywords |
Variable structure system ; Sliding mode control ; Proof of Ukin's Theorem ; Diagonalization methods |
| Abstract |
In this note, a proof of Utkin's theorem is presented for a MI(Multi Input) uncertain linear case. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods are proved clearly and comparatively for MI uncertain linear systems. With respect to the sliding surface transformation and the control input transformation, the equation of the sliding mode i.e., the sliding surface is invariant. Both control inputs have the same gains. By means of the two transformation methods the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified. |