Geometric sliding mode control: the linear and linearized theory

The idea of sliding mode control for stabilization 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 equilibrium for a nonlinear system with a controllable linearization, the sliding subspace for a linearization gives rise to many local sliding submanifolds for the nonlinear system.