In this paper, we present a new control-theoretic framework to efficiently design balanced coordinated resource allocation algorithms in a network based on semistabilization theory for discrete-time stochastic linear systems together with compartmental modeling. Specifically, necessary and sufficient conditions for equivalent, control-theoretic characterizations of the proposed balanced coordinated resource allocation design problem are derived, which are based on a new notion of semiobservability and a new semistable Lyapunov equation. With this theory, we first unveil a striking connection between the balanced coordinated network resource allocation design problem and optimal semistable control theory by means of a stochastic optimal semistable control technique. Then we convert this optimal control-based design problem into a constrained, nonlinear optimization problem to look for possible numerical solutions to the original balanced coordinated resource allocation algorithm design problem. To this end, we propose a class of randomized swarm optimization-based numerical algorithms called multiagent coordination optimization to solve the constrained, nonlinear optimization problem. Finally, numerical results are provided to validate the proposed design framework and an application of a target search problem for threat detection and resource allocation is presented to further show the effectiveness of the proposed approach.