Constrained stabilization of periodic discrete-time systems via periodic Lyapunov functions

This article considers the problem of constrained stabilization of periodically time-varying discrete-time systems, or shortly, periodic systems. A modification of a recent result on periodic Lyapunov functions, which are required to decrease at every period rather than at every time instant, is exploited to obtain a new stabilizing controller synthesis method for periodic systems. We demonstrate that for the relevant class of linear periodic systems subject to polytopic state and input constraints, the developed synthesis method is advantageous compared to the standard Lyapunov synthesis method. An illustrative example demonstrates the effectiveness of the proposed method.