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In this paper, incremental exponential asymptotic stability of a class ofswitched Carath\'{e}odory nonlinear systems is studied based on the novelconcept of measure of switched matrices via multiple norms and the transactioncoefficients between these norms. This model is rather general and includes thecase of staircase switching signals as a special case. Sufficient conditionsare derived for incremental stability allowing for the system to beincrementally exponentially asymptotically stable even if some of its modes areunstable in some time periods. Numerical examples on switched linear systemsswitching periodically and on the synchronization of switched networks ofnonlinear systems are used to illustrate the theoretical results.

Contraction and incremental stability of switched Carath\'{e}odory systems using multiple norms