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This paper addresses the control and scheduling of embedded control systems with shared computation resources. The holistic system consisting of several linear plants, which are controlled by one single processor, is modeled as a switched control system. Based on quadratic Lyapunov function a method is introduced to design jointly schedule and control, which guarantees stability of all plants controlled by the processor. The proposed strategy is formulated as a constrained optimization problem, which firstly allows checking the feasibility of the stabilization of all plants by controlling them by one processor. Moreover, the solution of the constrained optimization problem contains the control gain and the necessary parameters for an appropriate online scheduling. The method is illustrated by an example.