The Response Bounds of Unknown Nonlinear Systems With Sinusoidal Input

This paper studies the bounds of the response of a class of nonlinear systems with sinusoidal inputs. The unknown nonlinear system is assumed to have a unique steady-state response for a given input under different initial conditions. The sufficient condition of this assumption is given, and the bounds of the transient response and the steady-state response are derived in the sense of 2-norm and L² norm, respectively. A simulation example is presented to demonstrate the results.