Switching Among Feedback-Linearizing Output Sets (Melds): Dwell-Time and Compatibility Guarantees

TL;DR

This paper analyzes switching among multiple feedback-linearizing output sets in nonlinear systems, providing dwell-time conditions and compatibility measures to ensure stable output tracking and bounded state errors.

Contribution

It introduces a novel analysis of output set switching in feedback-linearizable systems, including explicit dwell-time conditions and compatibility constants for stability guarantees.

Findings

Derived explicit dwell-time conditions for switching stability.

Introduced a reference-compatibility constant to measure output mismatch.

Validated results with a planar 3R manipulator example.

Abstract

We study switching among multiple square selections of output functions (melds) drawn from a deck of candidate outputs for nonlinear systems that are static feedback linearizable via outputs. Fixing an operating point, each meld induces a distinct feedback-linearizing coordinate chart defined on a common neighborhood. Switching between melds therefore produces state-dependent coordinate mismatches that are not captured by classical switched-system analyses. We quantify this effect through Lipschitz bounds on the cross-chart maps over a compact safe set and introduce a reference-compatibility constant that measures mismatch among reference families across melds. We derive an explicit dwell-time condition depending on controller decay rates and the compatibility constant, that guarantees exponential decay of the active-output tracking errors between switches, seamless tracking of outputs shared by consecutive melds, and uniform boundedness of the state error within the safe set. A planar 3R manipulator illustrates the results.