Stabilization of linear systems via low-order dynamic output feedback: a passification approach

In this paper we study the problem of rendering a linear time-invariant (LTI) system passive and stable via dynamic output feedback. In our methodology an additional system is parallel interconnected with the given system so that the overall system becomes minimum phase. The problem is solvable by the static output feedback algorithms (e.g. LMI). Then, the stabilizing gain matrix is easily obtained and an adaptive control scheme can be developed for that gain. The order of our dynamic controller is equal to that of the input of the given system. This work is a special case of the results of the dynamic output feedback passification of nonlinear systems, and is also related to the positive real problem and low-order stabilizing controller problem in the literature.