Reachable Set Estimation and Synthesis for Periodic Positive Systems

This paper investigates the problems of reachable set estimation and synthesis for periodic positive systems with two different exogenous disturbances. The lifting method and the pseudoperiodic Lyapunov function method are adopted for the estimation problem. The reachable set bounding conditions are proposed by employing Lyapunov-based inequalities and the S-procedure technique. Two optimization methods are used to minimize the bounding hyper-pyramids of the reachable set. In addition, the state-feedback controller design conditions that make the reachable set of closed-loop systems lie within a given hyper-pyramid are derived. Finally, numerical examples are presented to illustrate the validity of the obtained conditions.