Uniform Asymptotic Stabilization of Affine Periodic Discrete-Time Systems

In this article, we study the problem of asymptotic stabilization for nonlinear affine discrete-time control systems with periodic coefficients via state feedback. It is supposed that the origin of the free dynamic system is (non-asymptotically) stable. The method for constructing a damping control is extended from time-invariant systems to time varying periodic affine discrete-time systems. This method is based on the Krasovsky-La Salle invariance principle for periodic systems. Using this approach, we obtain sufficient conditions for uniform local and global asymptotic stabilization for those systems.