Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Extension of the Perron--Frobenius Theorem to Homogeneous Systems
SIAM Journal on Control and Optimization
Input-to-state stability for discrete-time nonlinear systems
Automatica (Journal of IFAC)
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A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exist points whose image under the monotone map is strictly smaller than the original point, in the component-wise partial ordering. Here it is shown how such points can be found numerically, leading to a recipe to compute order intervals that are contained in the region of attraction and where the monotone map acts essentially as a contraction. An important application is the numerical verification of so-called generalized small-gain conditions that appear in the stability theory of large-scale systems.