Uncertain LTI-models for linear control design of non-linear systems

Much attention in robust identification and control has been focused on linear low order models approximating high order linear systems. We consider the more realistic situation with a linear model approximating a non-linear system. We describe how a linear time invariant (LTI) model with unstructured uncertainty, i.e. a "band" of Nyquist curves, can be developed using a non-linear model error model. Applying standard linear robust control design to this uncertain LTI model will lead to a (non-linear) closed loop system with performance robustness guarantees (in terms of gain from disturbance to output) well in line with the objectives of the linear design. Clearly the design can be successful only if the linear model is a reasonably good approximation of the system. A particular aspect of the design process is to define a workable definition of "practical stability" for robust control design, with possibly non-linear model errors. We use affine power norms for that purpose