Equivalent control method singular correction

It is known that, when a system with sliding modes has different servomechanisms, equivalent control is undetermined. The mathematical model of such systems is a singularly perturbed differential equation system with discontinuous controls in which only a second-order sliding mode occurs. An algorithm for obtaining slow motion equations of such systems with arbitrary precision level with respect to the small parameter is proposed. This algorithm is applied to the correction of the equivalent control method. It is shown that, when the equivalent control method is asymptotically stable in the first approximation, solutions of the whole system are stable