Optimal H2 control of oscillations via derivative state constraints

Studied in the paper are the optimal H₂ controls of oscillatory systems via the constraints of the derivatives of state variables. It is shown that the derivative state constrained H₂ optimal control can be reduced to the standard H₂ optimal control problem with modified controlled output equation and the solution to the modified standard problem has salient features for controlling oscillatory systems. The incorporation of this approach with the stability degree specification scheme is also shown. The results show how to select the constraining weights in the standard modern control design of oscillatory systems that has been a tough subject to control in state space as well as in classical frequency domain. The verifications of the proposed schemes are given in an illustrative example