Stabilizability of Finite and Infinite Dimensional Bilinear Systems

摘要

The stabilizability of a general bilinear system in finite and infinite-dimensional spaces is considered. The stabilizing feedback controller is defined in such a way that the resulting system is of the variable-structure type with a stable sliding mode on a subspace of a state space. This leads to unbounded controls in the neighborhood of the set, but in many cases a simple perturbation of the switching manifolds leads to a bounded controller. In the finite-dimensional case, nonlinear control is discussed. The existence of switching manifolds defined by the solutions of polynomial equations is shown.