Stabilization of fixed modes in expansions of LTI systems

The objective of this note is to propose a method for stabilization of structurally fixed modes in expansions of LTI dynamic systems in the scope of overlapping decentralized control design based on the expansion/contraction framework, enabling successful design for a broader class of problems than considered so far. The method is based on a judicious choice of complementary matrices in the expanded space. Numerical examples are provided to illustrate simplicity and efficiency of the proposed approach.