dynamical system

Steplength thresholds for invariance preserving of discretization methods of dynamical systems on a polyhedron

  • Zoltán Horváth
  • Tamás Terlaky
  • Yunfei Song
    • Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , , , ,

    Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first positive zeros of a finite number of polynomial functions. Further, a simple and efficient algorithm is proposed to numerically … Read more

    Steplength Thresholds for Invariance Preserving of Discretization Methods of Dynamical Systems on a Polyhedron

  • Zoltán Horváth
  • Tamás Terlaky
  • Yunfei Song
    • Categories Control Applications, Convex and Nonsmooth Optimization, Polyhedra Tags , , ,

    Steplength thresholds for invariance preserving of three types of discretization methods on a polyhedron are considered. For Taylor approximation type discretization methods we prove that a valid steplength threshold can be obtained by finding the first positive zeros of a finite number of polynomial functions. Further, a simple and efficient algorithm is proposed to numerically … Read more

    A Novel Unified Approach to Invariance in Control

  • Zoltán Horváth
  • Tamás Terlaky
  • Yunfei Song
    • Categories Control Applications, Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    In this paper, we propose a novel, unified, general approach to investigate sufficient and necessary conditions under which four types of convex sets, polyhedra, polyhedral cones, ellipsoids and Lorenz cones, are invariant sets for a linear continuous or discrete dynamical system. In proving invariance of ellipsoids and Lorenz cones for discrete systems, instead of the … Read more