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针对二维多项式非线性系统,提出了基于特征根负定配置的镇定控制方法.引入自由多项式,克服系统状态矩阵描述的不惟一性,进而降低控制综合问题求解的保守性.将特征根负定配置问题转化成多项式正定性验证问题,控制器设计问题通过多项式分解最终可由半定规划工具数值求解.在所提出的处理方法的基础上,讨论了4类二维多项式非线性系统的镇定控制问题.仿真结果验证了所提出方法的有效性.
For the two-dimensional polynomial nonlinear system, a stabilization control method based on the negative definite configuration of the eigenvalues is proposed. By introducing a free polynomial to overcome the non-uniqueness of the system state matrix description, the conservation of the control comprehensive problems is reduced. The configuration problem is transformed into the polynomial positive qualitative verification problem, and the controller design problem can be solved numerically by semidefinite programming tools through polynomial decomposition. On the basis of the proposed method, the stabilization control problems of four kinds of two-dimensional polynomial nonlinear systems are discussed The simulation results verify the effectiveness of the proposed method.