On Existence of a Class of Partial States Feedback Stabilizing Law for Single-Input-Single-Output Linear LTI Systems and Its Applications

In this paper, the existence of a certain class of partial states feedback stabilization law for single input single output linear time-invariant (LTI) systems with the only knowledge of its relative degree is discussed. The results show that for minimum phase systems or open-loop asymptotic stable systems, there always exists such feedback control law and for non-minimum unstable systems or three types of special systems with relative degree not greater than 2, there doesn´t always exist such control law. The results also show that if the supposed stabilization law exists, then there will always be LTI compensators with the same order of such control law. The results is applied to study the existence of proportional-derivative like control for flexible structures and the existence of a certain type of adaptive stabilization law.