Uncertain LTI-models for Linear Control Design of Non-Linear Systems, Report no. LiTH-ISY-R-2808

Much attention in robust identi cation 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) closes loop system with performance robustness guarantees (in terms of gain from disturbances 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 reasonable good approximation of the system. A particular aspect of the design process is to de ne a workable de nition of practical stability for robust control design, with possibly non-linear model errors. We use a ne power norms for that purpose.