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.