Contents I. Introduction
Hybrid integrator-gain systems (HIGS) are hybrid control elements introduced in [1] to overcome fundamental limitations of linear time-invariant (LTI) control systems [2], [3]. A HIGS switches between an integrator mode and a gain mode so that a certain sector constraint is satisfied. To be specific, a HIGS is primarily designed to operate as an integrator, and it switches to the gain mode when its integrator dynamics tend to violate the sector constraint. The describing function of a HIGS has a phase lag of only 38.15 degrees, which is much smaller than the 90 degrees phase lag of an integrator. Reset elements including the Clegg integrators [4] and first-order reset elements [5], [6] also have such advantages. However, they generate discontinuous control signals which may cause chattering and degrade the system performance [7], while HIGS generate continuous control signals. HIGS controllers have attracted attention since it was introduced (e.g., see [8]–[13]) and have found application on wafer scanners [14] and atomic force microscopy [15], where the latter work was motivated by the negative imaginary property of HIGS.
