It is necessary to keep the closed-loop system stable in data-driven feedback tuning. A widely-used strategy is using stability criterions as the constraint while parameter updating. In this strategy, the conservatism of the stability constraint has great influence on the achievable convergence performance. In this paper, a less conservative stability constraint is proposed to improve the convergence rate of data-driven feedback tuning methods. Specifically, the proposed stability constraint is developed based on small gain theorem (SGT). The conservatism is reduced through extension of SGT and further reduced using the properties of H norm. Besides, an unbiased data-driven estimation method of H norm is employed to estimate the proposed stability constraint accurately. Simulations are conducted to test the performance of the proposed stability constraint. The results demonstrate that the proposed stability constraint is less conservative and contributes to higher convergence rate.

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