Periodicity and stability analysis of periodic switched positive systems

Abstract

Addressed in this study are the minimal period and stability issues of periodic switched positive systems. With the assumption that all the system matrices, delays and switching signal are periodic, it is shown that the considered switched system is also periodic with the minimal period being a divisor of the least common multiple of the periods of subsystems and switching signal, and an algorithm is presented to determine the minimal period. Then some necessary and sufficient exponential stability conditions are proposed for periodic switched positive systems. These conditions are also extended to a more general class of periodic switched systems. Finally, a numerical example with three cases is provided to demonstrate the effectiveness of the theoretical results and reveals two interesting facts: The system matrices of periodic positive systems are unnecessarily non-negative and system delays influence system stability. These facts imply that there exist some remarkable differences between general switched positive systems and periodic switched positive systems.