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This paper provides new linear matrix inequalities (LMI)-based formulae for mixed H 2 /H ∞ state-feedback synthesis of linear continuous-time systems with state delays of any size. The proposed delay-independent LMI-based conditions enable us to parameterize a memoryless state-feedback controller without involving the Lyapunov variables in the formula. Compared with previous results based on a common Lyapunov variable, the proposed formula provides less conservative results.

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A design strategy for linear parameter-varying (LPV) systems is considered in a two-degree-of-freedom (TDOF) control framework. First, a coprime factorization for LPV systems is introduced. Second, based on the coprime factorization, a TDOF control framework of linear timeinvariant systems is extended to that of LPV systems. Good tracking performance and good disturbance rejection are achieved by a feedforward controller and a feedback controller, respectively. Furthermore, each controller design problem can be formulated in terms of a linear matrix inequality related to the L2 gain performance. Finally, a simple design example is illustrated.