A generalised homogeneous solution for global stabilisation of a class of non-smooth upper-triangular systems

This paper investigates the problem of using small controls to globally stabilise a class of upper-triangular systems, including non-smooth systems. A generalised definition of homogeneity with new weights is employed to relax the existing restrictions imposed on the nonlinearities and enable the design of non-smooth stabilisers. By developing a more delicate design approach, small state feedback controllers are recursively constructed in a bottom-to-top fashion to globally stabilise the upper-triangular systems. In addition, a number of typical examples are discussed in order to illustrate that the proposed result not only encompasses several existing works under the same topic, but also solves the global stabilisation problem of more general upper-triangular systems using simpler controller structures.

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