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A kind of new linear matrix inequality (LMI)-based formulation is presented for multi- objective Hinfin/alpha-stability controller synthesis of linear time invariant (LTI) systems. New LMI-based conditions enable to parameterise controllers without involving the Lyapunov variables in the formulation. With this feature, multi-objective controllers can be designed, with non- common Lyapunov variables and two additional adjustable scalars. Furthermore, to find the minimum possible cost, LMI-based conditions can be solved by the grid of the space which is composed of these scalars. When compared with previous results based on a common Lyapunov function, this provides less conservative results. Finally, two numerical examples are included to illustrate the effectiveness of the proposals.