Passivity approach to stability analysis for nonlinear and time-varying dynamic systems

Stability of nonlinear and time-varying systems is studied by using passivity analysis. For this purpose, a nonlinear composite differential operator d(1) (x) = k(x)s and a nonlinear time-varying composite differential operator d(coproduct)(x,t) = k(x,t)sk(x,t) are introduced. Here s = (d)/(dt) is the ordinary differential operator and x denotes the state of the system under study. By using these composite differential operators, strictly passive nonlinear and/or time-varying systems are constructed. Then the conditions of asymptotic stability can be determined.