A Two-step LMI Scheme for H2 − H∞ Control Design

In this paper, a two-step H2 − H∞ control design scheme with guaranteed mixed H2 and H∞ performance is proposed. Different from the traditional H2/H∞ control, the proposed method designs an H2 controller for a nominal plant and then designs an extra Q operator to recover robustness in H∞ sense for the closed-loop system. When the system uncertainty occurs, operator Q is triggered by a residual signal due to the error between the nominal model and the actual plants, and an extra control signal is generated by operator Q to compensate the nominal H2 controller. It is noted that the proposed H2 − H∞ design scheme provides additional design freedom to reduce conservativeness, comparing with the traditional mixed H2/H∞ control. The control design in the Linear Matrix Inequality (LMI) approach is applied to synthesize the H2 − H∞ controller. Simulation results of a numerical example are given to demonstrate that H2 − H∞ control design is able to compensate the nominal H2 control and significantly improve system performance in the presence of system uncertainty. Moreover, two-step H2 −H∞ control renders better state responses than the traditional mixed H2/H∞ control.