Design and analysis of controllers for discontinuous dynamic systems by reshaping of Poincare map

Examines the problem of precise position control when the system being controlled has a dead zone and cannot be described with differentiable dynamics. The behavior of the system under proportional-integral-derivative (PID) control is analysed using the Poincare map, which shows the existence of a stable fixed point and a disjoint collection of intervals which are mapped to the desired position (the origin). The author also addresses the design and analysis of discontinuous control systems by the technique of reshaping of the Poincare map