Tools for Semiglobal Stabilization by Partial State and Output Feedback

Abstract

We develop tools for uniform semiglobal stabilization by partial state and output feedback. We show, by means of examples, that these tools are useful for solving a variety of problems. One application is a general result on semiglobal output feedback stabilizability when global state feedback stabilizability is achievable by a control function that is uniformly completely observable. We provide more general results on semiglobal output feedback stabilization as well. Globally minimum phase input--output linearizable systems are considered as a special case. Throughout our discussion we demonstrate the usefulness of considering local convergence separate from boundedness of solutions. For the former we employ a sufficient small gain condition guaranteeing convergence. For the latter we rely on Lyapunov techniques.