Robust mixed H2/H∞ control of time-varying delay systems with extended LMI

This paper studies robust performance analysis of H₂/H_infin control problem in time-varying systems. In the case where the state-space matrices of the system depend affinely on the uncertain parameters, it is known that recently developed extended or dilated linear matrix inequalities (LMIs) are effective to assess the robust performance in a less conservative fashion. This paper further probes into those preceding results and proposes a new form of extended LMIs for time-varying H₂/H_infin controllers synthesis. The new method enables us to parameterize controllers without involving the Lyapunov variables in the parameterization. The numerical simulations prove the validity of this framework.