Static output feedback simultaneous stabilisation via coordinates transformations with free variables

This study deals with simultaneous stabilisation of linear time-invariant systems via static output feedback by designing transformations of state vectors that contain free variables. The transformations reformulate each system as two interconnected systems, and one of the isolated subsystem is stabilised by choosing the free variable as a style of state feedback. Then the common feedback gain matrix can be determined if a linear matrix inequality system is feasible. This method does not concern any reduction or enlargement of matrix inequalities, and is effective for non-minimum phase systems. Numerical examples show the validity of the proposed algorithms for both continuous and discrete systems.