In this paper, a method for numerical solution of differential-algebraic equations (DAEs) in Hessenberg form is presented. In this method, a sliding surface proportional to systems index is defined that generates a complete equation to calculate algebraic variables. Since the sliding surface is stable, convergence of the distance from manifold constraint in DAE is satisfied. Finally, the proposed method is applied for some linear and nonlinear index-3 systems. Numerical solutions confirm the accuracy of the proposed technique.

Keywords: differential-algebraic equations, Hessenberg form, sliding mode control, constraint manifold tracking

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