Decomposition of the min-max multi-model problem via integral sliding mode

The concept of the integral sliding mode (ISM) is revised and applied for robustification of a linear time invariant min-max multi-model problem with uncertainties. Modified version of ISM ensures the insensitivity of the designed min-max control law with respect to matched uncertainty, starting from the beginning of the process, and guarantees that the unmatched part of uncertainties is minimized and not amplified. Proposed ISM dynamics allows to reduce the dimension [Nn] of the min-max control design problem to the space of unmatched uncertainties only of [Nn -(N -1)m] size. A numerical example illustrates that the suggested modification of the ISM dynamics does not change the min-max control as well as the value of the corresponding performance index.