Original manuscript: 2003/01/09
Manuscript last revised: 2003/08/18

The idea of sliding mode control for stabilisation is investigated to determine its geometric features. A geometric definition is provided for a sliding submanifold, and for various properties of a sliding submanifold. Sliding subspaces are considered for linear systems, where a pole placement algorithm is given that complements existing algorithms. Finally, it is shown that at an equilibrium for a nonlinear system with a controllable linearisation, the sliding subspace for a linearisation gives rise to many local sliding submanifolds for the nonlinear system. This theory is exhibited on the standard pendulum/cart system.

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