Uniform Local and Global Asymptotic Stabilization of Nonlinear Periodic Discrete-Time Systems by State Feedback

In this article, we study the problem of uniform local and global asymptotic stabilization of the origin for nonlinear discrete-time control systems with periodic coefficients via state feedback. It is assumed that the origin of the free dynamic system is Lyapunov stable. The approach is based on the Krasovsky–La Salle invariance principle for discrete-time periodic systems. The stabilizing control law is constructed by means of applying bounded feedback design technique previously developed for time-invariant nonlinear systems in combination with the stabilizing state feedback control schemes proposed before for discrete-time periodic systems. Sufficient conditions for uniform local and global asymptotic stabilization for nonlinear discrete-time systems with periodic coefficients are obtained. The earlier corresponding results for nonlinear time-invariant systems and for affine periodic systems are generalized and strengthened.