Robust regulation with an H<inf>∞</inf> constrain for linear two-time scale systems

In this paper, the problem of robust multi-objective control design with an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> constrain is studied for a class of linear two-time scale systems. The design is based on a new modelling approach under the assumption of norm-boundedness of the fast dynamics. In this method, a portion of the fast dynamics is treated as a norm-bounded perturbation in the design by its maximum possible gain. In this view, the problem of robust multi-objective control design is performed only for the certain dynamics of the two-time scale system, whose order is less than that of the original system. One illustrative example is used to demonstrate the validity of the proposed approach.