A Constructive Approach to Local Stabilization of Nonlinear Systems by Dynamic Output Feedback

Abstract

The note considers the problem of local stabilization of nonlinear systems by dynamic output feedback. A new concept, namely, local uniform observability of feedback control law, is introduced. The main result is that if a nonlinear system is th-order approximately stabilizable by a locally uniformly observable state feedback, then it is stabilizable by dynamic output feedback. Based on the approximate stability, a constructive method for designing dynamic compensators is presented. The design of the dynamic compensators is beyond the separation principle and can handle systems whose linearization might be uncontrollable and/or unobservable. An example of nonminimum phase nonlinear systems is presented to illustrate the utility of the results.Index Terms-Dynamic output feedback, local uniform observability, nonlinear systems, nonminimum phase systems, stabilization.

Bifurcation stabilization of nonlinear systems by dynamic output feedback with application to rotating stall control

“…The concept of approximation stability plays an important role in the equilibrium point stabilization of nonlinear systems [18,21], but it cannot be directly applied to the bifurcation stabilization, since the bifurcation stability may be easily spoilt by parameter perturbation. The concept of approximation stability plays an important role in the equilibrium point stabilization of nonlinear systems [18,21], but it cannot be directly applied to the bifurcation stabilization, since the bifurcation stability may be easily spoilt by parameter perturbation.…”

“…Uniform observability of a function has been introduced in [17,18], in which the considered functions do not depend on input variable u and parameter μ. The phrase "with respect to (1)" in Definition 4 will be omitted if there is no confusion.…”

“…We introduce the concepts of uniform observability of the inverse of a function of state and input and N -orderinput-to-state bifurcation stability. In the cases where some state variables are not measurable, output feedback control design of nonlinear systems becomes necessary and has been studied in different ways [17,18]. As an example, we apply the general theory to active control of rotating stall in axial flow compressors by designing a stabilizing dynamic compensator for the three-state Moore-Greitzer model with a class of cubic compressor characteristics.…”

“…The methods presented in [5,10,11,16] are applicable to dynamic output feedback bifurcation stabilization only in the case where the dimension of the dynamic compensator is known. In the cases where some state variables are not measurable, output feedback control design of nonlinear systems becomes necessary and has been studied in different ways [17,18]. Thus, the theory on bifurcation stabilization via dynamic output feedback is far from complete.…”

“…Thus, the theory on bifurcation stabilization via dynamic output feedback is far from complete. In the output feedback control design related to center manifold, two concepts of the approximation stability [18,21] and uniform observability [17,18] have often been used. In the cases where some state variables are not measurable, output feedback control design of nonlinear systems becomes necessary and has been studied in different ways [17,18].…”