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

In this paper, a two-step H<inf>2</inf> − H<inf>∞</inf> control design scheme with guaranteed mixed H<inf>2</inf> and H<inf>∞</inf> performance is proposed. Different from the traditional H<inf>2</inf>/H<inf>∞</inf> control, the proposed method designs an H<inf>2</inf> controller for a nominal plant and then designs an extra Q operator to recover robustness in H<inf>∞</inf> 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 H<inf>2</inf> controller. It is noted that the proposed H<inf>2</inf> − H<inf>∞</inf> design scheme provides additional design freedom to reduce conservativeness, comparing with the traditional mixed H<inf>2</inf>/H<inf>∞</inf> control. The control design in the Linear Matrix Inequality (LMI) approach is applied to synthesize the H<inf>2</inf> − H<inf>∞</inf> controller. Simulation results of a numerical example are given to demonstrate that H<inf>2</inf> − H<inf>∞</inf> control design is able to compensate the nominal H<inf>2</inf> control and significantly improve system performance in the presence of system uncertainty. Moreover, two-step H<inf>2</inf> −H<inf>∞</inf> control renders better state responses than the traditional mixed H<inf>2</inf>/H<inf>∞</inf> control.

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