• An example with interesting controllability and stabilisation properties 

      Hirschorn, Ron M.; Lewis, Andrew D. (2005)
      A simple three-state system with two inputs is considered. The system's controllability is determined using properties of vector-valued quadratic forms. The quadratic structure is then used as the basis for the design of ...
    • Geometric local controllability: second-order conditions 

      Hirschorn, Ron M.; Lewis, Andrew D. (2002)
      In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from ...
    • Geometric sliding mode control: The linear and linearised theory 

      Hirschorn, Ron M.; Lewis, Andrew D. (2002)
      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 ...
    • High-order variations for families of vector fields 

      Hirschorn, Ron M.; Lewis, Andrew D. (2002)
      Sufficient conditions involving Lie brackets of arbitrarily high-order are obtained for local controllability of families of vector fields. After providing a general framework for the generation of high-order ...