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This article deals with the problem of mean square stability of discrete-time networked control systems (NCSs) over a communication channel subject to packet dropout. By introducing a parameter-independent slack variable with lower triangular structure, the existence of a static output feedback controller is formulated in the form of linear matrix inequalities. Neither equality constraint nor iterative algorithm is involved through the derivation of the controller. Furthermore, a new algorithm is proposed to obtain the admissible packet dropout probability bound for the given controller gain. This is particularly important in the co-design of controller and scheduling for NCSs. The simplicity of the methods is demonstrated by numerical examples. [ABSTRACT FROM AUTHOR]