Abstract
A matrix is called totally positive (TP) if all its minors are positive. A linear time-varying system is called a totally positive discrete-time system (TPDTS) if the matrix defining its evolution is TP for all time. It was recently shown that this can be used to prove strong asymptotic properties of certain time-varying nonlinear discrete-time systems. However, this requires establishing that a line integrals of the Jacobian of the nonlinear system is TP. We derive several new conditions guaranteeing that the line integral of a matrix is TP and demonstrate how this yields interesting classes of nonlinear systems that are guaranteed to entrain to a periodic excitation.
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