Transverse feedback linearization with partial information for single-input systems

TL;DR

This paper develops a method for stabilizing invariant sets in nonlinear single-input control systems using output feedback, by transforming systems into a normal form that simplifies controller design.

Contribution

It provides necessary and sufficient conditions for feedback equivalence to a normal form tailored for output feedback stabilization of invariant sets.

Findings

Conditions for feedback equivalence are established.

Normal form facilitates output feedback controller design.

Applicable to nonlinear, control-affine systems with invariant sets.

Abstract

This paper is motivated by the problem of asymptotically stabilizing invariant sets in the state space of control systems by means of output feedback. The sets considered are smooth embedded in submanifolds and the class of system is nonlinear, finite-dimensional, autonomous, deterministic, single-input and control-affine. Given an invariant set and a control system with fixed output, necessary and sufficient conditions are presented for feedback equivalence to a normal form that facilities the design of output feedback controllers that stabilize the set using existing design techniques.