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This paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback. The problem is formulated as a pseudoconvex optimization problem with robustness measure: i.e., the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment. Two coupled recurrent neural networks are applied for solving the formulated problem in real time. In contrast to existing approaches, the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables. Simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority.