Controllability and Observability of Linear Matrix-Second-Order Systems

Abstract

This paper studies the controllability and observability of the system Mq¨ + Gq˙ + Kq = Bu, where M is symmetric and positive-definite, G is skew-symmetric and K is symmetric. In all cases, the output equation is y = Pq + Rq˙. This special structure is exploited to derive relatively simple controllability and observability conditions which are shown to provide important insights on the modal behavior of the system and to furnish information on the number and positioning of sensors and actuators.