Extension of the Krylov-Bogoliubov method and its application to the decay rate analysis of nonlinear control algorithms

An extension of the Krylov-Bogoliubov method and of the harmonic linearization method for approximating second order nonlinear systems with fast variation of damping factor and frequency of oscillation is revisited and a solution method involving a power series approach is proposed, which makes it easy for the extended asymptotic method to be applied to other damped nonlinear systems. Furthermore, the application of the method to the analysis of the decay rate of the nonlinear solution is presented. A performance measure for the analysis of the decay rate for nonlinear systems is proposed and exemplified on two nonlinear control algorithms, linear constrained control and constrained soft variable structure control with implicit Lyapunov functions.