Stabilization of Nonlinear Systems Using Linear Observers

Abstract

In this paper, it is shown that a linear observer can always be designed to stabilize a nonlinear system which contains a Lur’e type nonlinearity in the sector [0 , k], where k is finite, if both the output of the nonlinearity and a completely observable output of the linear portion are available as inputs to the observer. In case a completely observable output is not available from the linear portion, stabilization is shown to be possible if the original linear approximation of the system is asymptotically stable or those state variables corresponding to the unstable eigenvalues are available. It is also established that a linear observer can be used to guarantee that a finite region of asymptotic stability exists for a plant described by a more general set of nonlinear equations, and in some cases the domain of asymptotic stability can be made as large as desired.