Singular perturbation analysis of the step-response matrices of a class of linear multivariable systems

Singular perturbation methods are used to demonstrate that the step-response matrices of linear multivariable systems containing small ‘parasitic” elements have a distinctive structure which guarantees the robustness of both non-adaptive and adaptive controllers for such systems incorporating step-response matrices. The significance of these results in relation to the modelling of multivariable plants with ‘fast” actuators and sensors is illustrated, and their validity is demonstrated by considering a typical gas-turbine jet engine.