On the Prevalence of Linear Parameter Varying Systems

This note comments on a number of recent gain-scheduling approaches which assume that the plant to be controlled is in so-called linear or quasi-linear parameter-varying form. In the first part of the note it is shown that present theory does not support the reformulation of nonlinear systems into linear/quasi-linear parameter-varying form without, in general, considerable restrictions either on the class of nonlinear systems considered or on the allowable operating region. The shortcomings of a popular ad hoc reformulation approach are also demonstrated. In the second part of the note, it is shown that, by employing velocity-based formulation, a very general class of nonlinear systems can, indeed, be transformed into linear/quasi-linear parameter-varying form. It is emphasised that this transformation is global in nature, with no restriction to near equilibrium operation.

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