Disturbance tolerance and H∞ Control of Port-Controlled Hamiltonian systems in the presence of actuator saturation

This paper investigates the disturbance tolerance and H
_∞
control of multi-input Port-Controlled Hamiltonian (PCH) systems in the presence of actuator saturation which may be not open-loop stable. A simple condition is derived under which trajectories starting from the origin will remain inside an ellipsoid. The disturbance tolerance ability of the closed-loop system under a given feedback control law is measured by the size of this ellipsoid. Based on the above mentioned condition, the problem of disturbance tolerance can be expressed in the form of the linear matrix inequalities (LMIs) optimization problem with constraints. In addition, an H
_∞
control approach is presented to attenuate the disturbances, and disturbance rejection ability in terms of L
₂
gain is also determined by the solution of an LMI optimization problem. Study of an illustrative example with simulations shows the effectiveness of the methods proposed.