Weak stability of nonlinear repetitive processes

Abstract

This paper considers nonlinear discrete and differential repetitive processes using the state-space model setting. These processes are a particular case of 2D systems that have their origins in the modeling of physical processes. Previous research has developed the exponential stability property but for some applications this property may be too strong. To address this issue, the new property of stability in a weak sense is defined and a vector Lyapunov function method was used to obtain sufficient conditions for the existence of this property. Based on these results the property of weak passivity is introduced and used, together with a vector storage function, to develop a new method for output based control law design. An example of a system with nonlinear actuator dynamics and a numerical study of iterative learning control design for a rigid single link robot are given to demonstrate the eventual effectiveness of these new results for applications.