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This paper fills a gap in the literature by considering a joint sensor andactuator configuration problem under the linear quadratic Gaussian (LQG)performance without assuming a predefined set of candidate components.Different from the existing research, which primarily focuses on selecting orplacing sensors and actuators from a fixed group, we consider a more flexibleformulation where these components must be designed from scratch, subject togeneral-form configuration costs and constraints. To address this challenge, wefirst analytically characterize the gradients of the LQG performance withrespect to the sensor and actuator matrices using algebraic Riccati equations.Subsequently, we derive first-order optimality conditions based on theKarush-Kuhn-Tucker (KKT) analysis and develop a unified alternating directionmethod of multipliers (ADMM)-based alternating optimization framework toaddress the general-form sensor and actuator configuration problem.Furthermore, we investigate three representative scenarios: sparsity promotingconfiguration, low-rank promoting configuration, and structure-constrainedconfiguration. For each scenario, we provide in-depth analysis and developtailored computational schemes. The proposed framework ensures numericalefficiency and adaptability to various design constraints and configurationcosts, making it well-suited for integration into numerical solvers.

A Unified Alternating Optimization Framework for Joint Sensor and Actuator Configuration in LQG Systems