Tracking observer/controller for a relatively large class of systems with hysteresis and without velocity measurement

In this work, we present an observer and controller for a class of plants with a relatively large class of hysteresis and without velocity measurement. For these considered classes of hysteretic systems, we propose and present an observer/controller that estimates or observes both the hysteresis state and the velocity and drives the position tracking error to zero. We prove that the combined tracking error and observer errors converge to zero, non-globally. Additionally, in the process, we verify that the convergence in [B.J. Driessen, V.M. Duggirala, Globally asymptotic and locally exponential tracking observer/controller for a relatively large class of systems with hysteresis, Journal of Intelligent and Robotic Systems 50 (2) (2007) 207–215] is actually semi-globally exponential (here meaning: exponential on any arbitrarily large compact set, for a fixed set of gains), while [B.J. Driessen, V.M. Duggirala, Globally asymptotic and locally exponential tracking observer/controller for a relatively large class of systems with hysteresis, Journal of Intelligent and Robotic Systems 50 (2) (2007) 207–215] claimed only globally asymptotic and locally exponential. The method, in the present paper, of combining asymptotic bound relations to prove that the observer error converges to zero appears to be a new alternative to the often difficult approach of trying to find a single Lyapunov function that simultaneously covers all of the error variables.