Contraction-Based Control of Switched Nonlinear Systems Using Dwell Times and Switched Contraction Metrics

This letter presents the contraction-based control of switched nonlinear systems to time varying references under dwell time conditions. The overall approach is to study the differential dynamics of switched subsystems, using switched contraction metrics, for a corresponding switched nonlinear system, and use properties of the Riemannian energy to draw conclusions on the incremental stability of the collective dynamics. The result is the formulation of conditions on the switching signal that guarantee contraction of the overall system with a specified contraction rate. Reference-independent synthesis and implementation details for a novel switched contraction-based tracking controller, based on the proposed framework, are also provided. An illustrative example is presented to demonstrate the proposed approach.