Optimal stabilization using Lyapunov measure

The focus of the paper is on the computation of optimal feedback stabilizing control for discrete time control system. We use Lyapunov measure, dual to the Lyapunov function, for the design of optimal stabilizing feedback controller. The linear Perron-Frobenius operator is used to pose the optimal stabilization problem as an infinite dimensional linear program. Finite dimensional approximation of the linear program is obtained using set oriented numerical methods. Simulation results for the optimal stabilization of periodic orbit in one dimensional logistic map are presented.