To address the prescribed performance formation control issues for general high-order linear swarm systems under the condition of switching topologies, an optimized formation design and analysis method adaptive to communication topology changes is proposed. Firstly, a global formation performance optimization index is constructed, and a control protocol with adaptive communication weights is designed. Relying on orthogonal transformation, the system dynamics are decomposed into formation center dynamics and formation error dynamics. Furthermore, by leveraging the dynamics of the formation center, the explicit formulation for the formation center function is deduced, and it is proven that this function is unaffected by time-varying weights or topology switching. For formation error dynamics, a quadratic Lyapunov function is constructed using coordination errors and a positive definite matrix. By correlating the performance index with the Lyapunov derivative, the relationship between the performance upper bound and matrix variables is established. Combined with preset performance constraints, linear matrix inequality conditions are obtained to form design criteria, and the explicit formulation of performance cost is obtained, along with methods to adjust gain matrices and the cost. Finally, a formation simulation experiment with five agents demonstrates the effectiveness of the proposed method.