Numerical stabilisation of non-linear systems: Exact theory and approximate numerical implementation

In this paper, a theoretical background is presented for the stabilisation of non-linear systems. A numerical implementation is then proposed. The cla ss of systems concerned with the proposed practical approach is quite large and contains all flat systems as a particular subset. The stabilising stra tegy is based on path generation strategy and avoids the integration of the differential system. The numerical implementation extensively uses the int erpolation on a function basis. Two examples of systems known to be hard to stabilise are given to illustrate the proposed algorithm.