A Modified Design for the VS-MRAC Based on the Indirect Approach: Stability Analysis

Abstract Recently, an alternative to achieve a robust controller that provides a straightforward and intuitive design and tuning of its parameters named Indirect Variable Structure Model Reference Adaptive Controller (IVS-MRAC) was presented for relative degree one LTI plants, suggesting to be globally asymptotically stable with superior transient behavior and disturbance rejection properties. Its novelty is in the procedure to obtain the bounds for the relay's amplitudes, used in the switching laws. These bounds are now associated with the plant parameters, instead of the controller parameters. In this paper, a modification is made on the plant high frequency gain switching law, in order to develop a first formal stability analysis, considering the presence of input disturbances and unmodeled dynamics. It is shown that the overall system error is stable with respect to some small residual set.

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