A new stabilizing feedback design method is proposed in this paper for time delayed polynomial systems with a linear input structure. The task is to transform the open loop system to a time delayed complex balanced kinetic system by using a polynomial state feedback structure which guarantees stability with arbitrary time delays.

It is shown that the required computations can be performed by simple linear programming, when the only goal is the semistability of the chosen equilibrium point. If one wants to achieve additionally the uniqueness of the closed loop equilibrium point to ensure local asymptotic stability, then the extended optimization problem requires the application of semidefinite programming. The existence of the solution and computability of the feedback do not depend on the magnitude of the delays.

It is shown that involving additional monomials into the feedback beyond the ones contained in the open-loop model does not improve the solvability of the semistabilization problem, but it may ensure the uniqueness of the prescribed complex balanced equilibrium point. Thus, two variants of a systematic method are proposed to find appropriate extra monomials for the feedback. One of these requires to solve a linear programming optimization problem even in this extended case.

针对具有线性输入结构的时滞多项式系统，提出了一种新的稳定反馈设计方法。任务是通过使用多项式状态反馈结构将开环系统转换为时间延迟的复杂平衡动力学系统，该结构可确保任意时间延迟的稳定性。

结果表明，当唯一的目标是所选平衡点的半稳定性时，可以通过简单的线性编程来执行所需的计算。如果要另外获得闭环平衡点的唯一性以确保局部渐近稳定性，则扩展的优化问题需要应用半定规划。解决方案的存在和反馈的可计算性不取决于延迟的大小。

结果表明，除了开环模型中包含的附加单项式之外，还不能将其他单项式包含在反馈中，这不会提高半稳定问题的可解性，但是可以确保规定的复杂平衡点的唯一性。因此，提出了一种系统方法的两个变体，以找到适当的额外单项式反馈。其中之一要求即使在这种扩展情况下也要解决线性规划优化问题。