Structure of expansion-contraction matrices in the inclusion principle fordynamic systems

This paper characterizes a general structure of complementary matrices invo lved in the input-state-output inclusion principle for linear time invarian t dynamic systems. Aggregations and restrictions are adopted as two practic ally important classes within this scheme. Further, contractibility conditi ons for feedback controllers are presented, including the decentralized con trol design. The identified structure enables the formulation of conditions on the complementary matrices which can be useful for analysis and synthes is of control problems.