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This article presents a utilization of viscoelastic damping to reduce control system complexity for strain-actuated solar array (SASA) based spacecraft attitude control systems (ACSs). SASA utilizes intelligent structures for attitude control, and is a promising next-generation spacecraft ACS technology with the potential to achieve unprecedented levels of pointing accuracy and jitter reduction during key scientific observation periods. The current state-of-the-art SASA implementation utilizes piecewise modeling of distributed piezoelectric (PZT) actuators, resulting in a monolithic structure with the potential for enhanced ACS reliability. PZT actuators can operate at high frequencies, which enables active vibration damping to achieve ultra-quiet operation for sensitive instruments. Relying on active damping alone, however, requires significant control system complexity, which has so far limited adoption of intelligent structures in spacecraft control systems. Here we seek to understand how to modify passive system design in strategic ways to reduce control system complexity while maintaining high performance. An integrated physical and control system design (codesign) optimization strategy is employed to ensure system-optimal performance, and to help understand design coupling between passive physical aspects of design and active control system design. In this study, we present the possibility of utilizing viscoelastic material distributed throughout the SASA substructure to provide tailored passive damping, intending to reduce control system complexity. At this early phase of study, the effect of temperature variation on material behavior is not considered; the study focuses instead on the design coupling between distributed material and control systems. The spatially-distributed design of both elastic and viscoelastic material in the SASA substructure is considered in an integrated manner. An approximate model is used that balances predictive accuracy and computational efficiency. This model approximates the distributed compliant SASA structure using a series of rigid links connected by generalized torsional springs and dampers. This multi-link pseudo-rigid-body dynamic model (PRBDM) with lumped viscoelastic damping models is derived, and is used in numerical co-design studies to quantify the tradeoffs and benefits of using distributed passive damping to reduce the complexity of SASA control systems.