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Passivity Index for Switched System Design

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Executive Summary

This paper presents a framework for control design of general nonlinear switched systems using passivity and two passivity indexes. Background material will be presented on traditional passivity for continuously varying systems, the concept of a passivity index, and passivity theory for switched systems. The passivity index concept will then be generalized to apply to switched systems to measure the degree of passivity in a system. It will be shown that when the passivity indexes exist, controllers can be designed to yield stable systems using the indexes. Two special cases are given for designing controllers for linear switched systems. The final result will then be presented showing that the passivity indexes can be used to design controllers for general non-linear switched systems.

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