Robustness of Uncertain Switching Nonlinear Feedback Systems Against Large Time-Variation

For a multiple-input–multiple-output (MIMO) nonlinear feedback system, the robustness against uncertain time-variation (slow or infrequently large) in the feedback loop is investigated in an input–output framework. A couple of sufficient conditions in terms of bounds on average rates of time-variation for the system to be stable are derived. The conditions provide a useful tool for designing adaptive controllers for systems against uncertain large time-variation.