Stability and convergence analysis for a class of nonlinear passive systems

A systematic and general method that proves state boundedness and convergence to nonzero equilibrium for a class of nonlinear passive systems with constant external inputs is developed. First, making use of the method of linear-time-varying approximations, the boundedness of the nonlinear system states is proven. Next, taking advantage of the passivity property, it is proven that a suitable switching storage function can be always obtained to show convergence to the nonzero equilibrium by using LaSalle´s Invariance Principle. Numerical and simulation results illustrate the proposed theoretical analysis.