Traditionally, a dynamic system is first designed then its controller is designed in a sequential process, which offers many organizational and computational advantages. However, this sequential design approach may not lead to system optimality compared to the combined design, or co-design, of the dynamic system and its controller. It has been proposed that a control proxy function (CPF) be used in the first step of this sequential design process to achieve, or approach, system-optimality. This paper considers the use of a CPF based on controllability and observability Gramians and a balanced realization to ensure the design of the dynamic system for both ease of control and estimation. The proposed approach is illustrated using an example of linear quadratic design for combined passive and active vibration control.

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