A sufficient condition for the stability of linear time varying learning control systems: a robotic application

L. Hideg et al. (1990) described an equivalent time domain condition for learning control stability and compared it to the well known frequency domain condition (J. Craig, 1988). Here the authors expand the class of learning controls systems and plants whose stability can be studied with the time domain formulation. The stability condition considers a linear time-varying single-input system with dynamics inspired by a robot model. The fundamental learning control formulations are reviewed. The authors present the standard Lyapunov function, the difference Lyapunov, and, a reduction strategy on that difference Lyapunov and describe the sufficient conditions for stability. The application to a robot system is outlined, showing the sufficient conditions for stability found here are quite broad and robust