A relaxation of Lyapunov conditions and controller synthesis for discrete-time periodic systems

This paper proposes a novel approach to stability analysis and controller synthesis for discrete-time periodically time-varying systems. Firstly, a relaxation of standard Lyapunov conditions is derived. This leads to a less conservative Lyapunov function that is required to decrease at every period, rather than at each time instant. Secondly, several solutions for synthesizing such periodic control Lyapunov functions are presented. These solutions make use of on-line optimization and can be formulated as a semi-definite program for constrained linear periodic systems. An example illustrates the effectiveness of the developed method.