Max- and Sum-Separable Lyapunov Functions for Monotone Networks with Balancing Kinetics

This paper investigates max- and sum-separable Lyapunov functions for monotone networks exhibiting balancing kinematics. Input-to-state stability is sought for internal stability and disturbance attenuation generalizing operator-norms nonlinearly. For linear networks it is known that max- and sum-separable Lyapunov functions can be expressed analytically with right- and left-eigenvectors. This paper discusses extensions of the formulas to nonlinear networks. The main target is non-identical balancing kinematics for which analytical solutions have not been available. It is shown that max- and sum-separable construction is no more given by eigenvectors, but it still accepts closed-form expressions.