In this paper, we will investigate the robust switching control problem for switched linear systems by using a class of composite quadratic functions, the min (of quadratics) function, to improve performance and enhance control design flexibility. The robustness is reflected in two prospectives including the ℋ performance and arbitrary switching of subsystems. A hysteresis min-switching strategy is employed to orchestrate the switching among a collection of controllers. The synthesis conditions for both state feedback and output feedback control problems are derived in terms of a set of linear matrix inequalities (LMIs) with linear search over scalar variables. The proposed min function based approach unifies the existing single Lyapunov function based method and multiple Lyapunov function based method in a general framework, and the derived LMI conditions cover the existing LMI conditions as special cases. Numerical studies are included to demonstrate the advantages of the proposed control design approach.

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