Design of Stable Time-varying Sliding Mode System

In this paper, we present a new time-varying sliding mode system that guarantees stable error convergence. The previous papers have dealt with stability of the time-varying sliding mode system by point-wisely investigating the stability of time-invariant system every time. However, it may be unstable even though it guarantees time-invariant stability every time, We designed the time-varying sliding surface so that the resultant time-varying system on sliding mode may be Stable. The initial sliding surface is obtained so that shifting distance of the surface may be minimized with respect to an initial error, and the intercept is produced so that the surface may pass the initial error.