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A methodology for the synthesis of gain scheduling controllers, capable of stabilising a class of nonlinear systems, is proposed in this paper. The technique is based on the spatial discretization of the state-space, considering only a subset of the states, generating an approximate dynamics dependent on time-varying parameters. The relationship between the stability of both the original and approximation dynamics is shown through a convex condition, which is then used to develop the proposed synthesis methodology. The computed controllers assure the local stability within a known region and can be obtained by the resolution of a set of convex conditions. A series of numerical experiments illustrate the validity of the technique.

Synthesis of gain scheduling controllers for a class of nonlinear systems based on a spatial discretization procedure