Stability of periodically time-varying systems: Periodic Lyapunov functions

This paper proposes a novel approach to stability analysis of discrete-time nonlinear periodically time-varying systems. The contributions are as follows. Firstly, a relaxation of standard Lyapunov conditions is derived. This leads to a less conservative Lyapunov function that is required to decrease at each period rather than at each time instant. Secondly, for linear periodic systems with constraints, it is shown that compared to standard Lyapunov theory, the novel concept of periodic Lyapunov functions allows for the calculation of a larger estimate of the region of attraction. An example illustrates the effectiveness of the developed theory.