Robust Asymptotic Stabilization of Nonlinear Systems with Non-Hyperbolic Zero Dynamics

In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models.Comment: 30 pages. Preliminary versions accepted at the 47th IEEE Conference on Decision and Control, 200

Control Lyapunov Functions and Stabilization by Means of Continuous Time-Varying Feedback

For a general time-varying system, we prove that existence of an "Output Robust Control Lyapunov Function" implies existence of continuous time-varying feedback stabilizer, which guarantees output asymptotic stability with respect to the resulting closed-loop system. The main results of the present work constitute generalizations of a well-known result towards feedback stabilization due to J. M. Coron and L. Rosier concerning stabilization of autonomous systems by means of time-varying periodic feedback.Comment: Submitted for possible publication to ESAIM Control, Optimisation and Calculus of Variation

Robust Asymptotic Stabilization of Nonlinear Systems With Non-Hyperbolic Zero Dynamics

International audienceWe present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to design locally Lipschitz stabilizers under conditions which only rely upon a partial detectability assumption on the controlled plant, by obtaining a robust stabilizing paradigm which is not based on design of observers and separation principles. The main design idea comes from recent achievements in the field of output regulation and specifically in the design of nonlinear internal models

Non-Uniform in Time Robust Global Asymptotic Output Stability for Discrete-Time Systems

In this paper the notions of non-uniform in time Robust Blobal Asymptotic Output Stability (RGAOS) and Input-to-Output Stability (IOS) for discrete-time systems are studied. Characterizations as well as links between these notions are provided. Particularly, it is shown that a discrete-time system with continuous dynamics satisfies the non-uniform in time IOS property if and only if the corresponding unforced system is non-uniformly in time RGAOS. Necessary and sufficient conditions for the solvability of the Robust Output Feedback Stabilization (ROFS) problem are also given.Comment: Submitted to the International Journal of Robust and Nonlinear Contro