Abstract
In this paper the local stability of relay feedback systems is considered. Concerning the local stability problem, the Tsypkin's conjecture is well known. Namely, if the linearized system is asymptotically stable for large gain including infinity, the original relay feedback system is locally asymptotically stable. The intuitive reasoning for the conjecture is that the saturating nonlinearity that is linear at the origin should approach the relay nonlinearity as the magnitude of the linear gain goes to infinity. The conjecture is verified to be correct by D.V. Anosov in the finite-dimensional cases.
The paper considers the Volterra integral equation and shows that the Typkin's conjecture is also valid under suitable conditions concerning the integral kernel. The results obtained here guarantee that the linearization for stability is applicable for the relay feedback systems containing the distributed parameter systems.
