Stability problem of a periodically varying system

Abstract

In this paper we investigate the problem of stability for periodically time-varying systems. This study is needed, for instance, to determine robustness and stability of repetitive learning systems used in the control of complex systems such as robotic manipulators. We use classical and new results for the stability of linear time-varying systems to re-establish an upper bound on the rate of parameter variations of the periodically time-varying systems, We then examine in detail the effects of these variations on the asymptotic and exponential stability of a special class of systems.