Stabilizability and Disturbance Rejection with State-Derivative Feedback

Abstract

In some practical problems, for instance in the control of mechanical systems using accelerometers as sensors, it is easier to obtain the state-derivative signals than the state signals. This paper shows that (i) linear time-invariant plants given by the state-space model matrices{A,B,C,D}with output equal to the state-derivative vector are not observable and can not be stabilizable by using an output feedback ifdet⁡(A)=0and (ii) the rejection of a constant disturbance added to the input of the aforementioned plants, consideringdet⁡(A)≠0, and a static output feedback controller is not possible. The proposed results can be useful in the analysis and design of control systems with state-derivative feedback.