Stabilisation by means of output feedback

This paper proposes a simple necessary condition for the stabilisation of an inherently unstable linear system with constant output feedback. This is a sign criterion obtained directly from the linear constraints on the attainable closed-loop characteristic polynomials when constant output feedback is employed. The condition is first established for single-input systems and then extended to multi-input systems, where the output-feedback matrices are restricted to have unity rank. Stabilisation with unconstrained output-feedback matrices is also discussed. Illustrative examples on stabilisation are given.