Stability of nonlinear feedback systems in a Volterra representation

Presented in this paper is a stability condition for a class of nonlinear f eedback systems where the plant dynamics can be represented by a finite ser ies of Volterra kernels. The class of Volterra kernels are limited to p-lin ear stable operators and may contain pure delays. The stability condition r equires that the linear kernel is non-zero and that the closed loop charact eristic equation associated with the linearized system is stable. Next, a s ufficient condition is developed to upper bound the infinity-norm of an ext ernal disturbance signal thereby guaranteeing that the internal and output signals of the closed loop nonlinear system are contained in L-infinity. Th ese results are then demonstrated on a design example. A frequency domain c ontroller design procedure is also developed using these results where the trade-off between performance and stability are considered for this class o f nonlinear feedback systems. Copyright (C) 2000 John Wiley & Sons, Ltd.