MIXED MONOTONE DECOMPOSITION OF DYNAMICAL-SYSTEMS WITH APPLICATION

The notions of mixed monotone decomposition of dynamical systems are i ntroduced. The fundamental idea is to make an elaborate use of the nat ural growth and decay mechanism inherent in the structure of a dynamic al systems to decompose its dynamics into increase and decrease parts, and thereby to constitute an augmented dynamical system as the so-cal led ''two-sided comparison system'' of the original one. The correspon ding two-sided comparison theorems show that the solution of the compa rison system gives lower and upper bounds of that of the original syst em. Therefore, the properties of a dynamical system can be obtained th rough the study of its two-sided comparison system. Compared with the conventional comparison method in literature, the mixed monotone decom position method developed herein takes in a natural way structural pro perties of dynamical systems into account instead of requiring strict conditions of (quasi-) monotonicity on them, and could yields refined, usually nonsymmetrical, state estimates, and thus is more suitable fo r systems with nonsymmetrical state constraints. As an application of the method, a sufficient condition is established for the global asymp totic stability of the trivial solution of a class of continuous-time systems with nonsymmetrical state saturation. The condition is given i n terms of coefficients and state saturation levers of such systems, a nd contains as a special case a recent result on systems with symmetri c state saturation in literature.