On stabilization and spectrum assignment in periodically time-varying continuous-time systems

This note discusses the stabilization and spectrum assignment problems in linear periodically time-varying (LPTV) continuous-time systems with sampled state or output feedback. The hybrid nature of the overall feedback system in this case imposes some carefulness in handling classical concepts related to purely LPTV continuous-time systems, In particular, this note points out the fact that the stabilization of such systems by periodic feedback gains with sampled state or output does not imply the relocation of the original characteristic exponents of the LPTV systems. It is also shown that the concept of monodromy matrix as extended to LPTV hybrid systems has not all the features of a true monodromy matrix