Stability criteria for off-diagonally monotone nonlinear dynamical systems

Abstract
Abstmet-This paper discu.~~~ the global stabiity of a nonlinear dynamical system X =f(x) in wbicb f is a locally Lipsddtz continuous off-diagonally monotone function and f( 0) > 0. Two results are prov& 1) if f is piecewise-linear function and if -f is an M-function, then a unique equilibrium point exists and it is globally asymptoticaUy stable; 2) if f is a nonlinear function with separate variables in the sense tbat f is given by A(x)=Zj",,f;.i(xj) for all i, and if -fis qn M-function satisfyingf(x*) =B for some nonnegative vector x*, then k* is globally asymptotically stable. These results are applied to the stabiity analyses of a large scale composite system and a compartmental system.

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