Subdivisions and triangulations of polytopes
Handbook of discrete and computational geometry
Semiconcave Control-Lyapunov Functions and Stabilizing Feedbacks
SIAM Journal on Control and Optimization
Control of Piecewise-Linear Hybrid Systems on Simplices and Rectangles
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Relatively Optimal Control: A Static Piecewise-Affine Solution
SIAM Journal on Control and Optimization
Control of systems integrating logic, dynamics, and constraints
Automatica (Journal of IFAC)
Propositional logic in control and monitoring problems
Automatica (Journal of IFAC)
A control problem for affine dynamical systems on a full-dimensional polytope
Automatica (Journal of IFAC)
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This paper studies a theoretical problem of whether continuous state feedback and affine feedback are equivalent from the point of view of making an affine system defined on a simplex reach a prespecified facet in finite time. We show that the two classes of feedbacks are equivalent. As a byproduct, new necessary and sufficient conditions for solvability based more directly on the problem data are obtained.