Removal of the terminal parameter-selection condition

Remove the parameter selection condition (c2), namely the requirement that the final control-design parameters satisfy c_{n,j}>K_{n-1,j} for every input channel, while retaining satisfaction of the modified performance constraints and boundedness of all closed-loop signals.

Background

Theorem 1 establishes the main closed-loop result only when the final-stage design parameters satisfy c_{n,j}>K_{n-1,j}, where K_{n-1,j} are unknown constants generated recursively in the analysis. Although Remark 5 states that the parameters can be chosen sufficiently large in principle, the conclusion explicitly identifies removal of this condition as unresolved future work. Eliminating it would reduce the conservatism and practical difficulty of parameter selection.

References

Future work includes the extension to non-BIBS stable or non-square MIMO nonlinear systems, and removal of parameter selection condition (\ref{c2}).

Low-Complexity Control Under Input Saturation and Performance Constraints: A Bidirectional Modification Scheme  (2609.00827 - Ni et al., 1 Sep 2026) in Section Conclusion; Theorem 1, condition (c2)