  This paper introduce the notion of output contraction that expands the
contraction notion to the time-varying nonlinear systems with output. It
pertains to the systems' property that any pair of outputs from the system
converge to each other exponentially. This concept exhibits a more expansive
nature when contrasted with another generalized contraction framework known as
partial contraction. The first result establishes a connection between the
output contraction of a time-varying system and the output exponential
stability of its variational system. Subsequently, we derive a sufficient
condition for achieving output contraction in time-varying systems by applying
the output contraction Lyapunov criterion. Finally, we apply the results to
analyze the output exponential stability of nonlinear time-invariant systems.
