Analysis and design of switching surface for nonlinear inear variable structure control systems

One of the main problems in variable structure control systems is finding the switching surface on which the controlled plant has a desired specific behaviour. This paper presents a new method for finding switching surfaces of nonlinear structure systems. Using this method, the designer first presents a system with the desired properties, then the switching the switching function σ(x) such that the switching surface
$S={x R^{n}\vert \sigma(x)=0}$
is coincident with the sliding motion in the given system. This method is applied to the design of the variable structure controller in a power system and the highest transient stability limitations are attained.