Abstract
Different methods of solution continuation for the system with discontinuous control and sliding modes are discussed in the paper. First, the systems with one discontinuity surface are discussed when the right-hand side of differential equation can take two values only for the selected state x and time t. According to Filippov method the right-hand side of sliding mode equation can be found in convex hull of these two values. Other five methods of solution continuation are developed under additional assumption about values of control on discontinuity surface. They led to sliding mode equations different from Filippov’s equations both for affine systems and systems nonlinear with respect to control. However, if we apply Filippov method based on the procedure of passing over to a convex hull considering additional assumptions of each method then the sliding mode equation is the same as for this method.
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