State feedback synthesis for polynomial systems with bounded disturbances
State feedback synthesis for polynomial systems with bounded disturbances
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DOI：
10.1109/cdc.2008.4738610
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发表时间：
2008-12
期刊：
影响因子：
--
通讯作者：
H. Ichihara
中科院分区：
文献类型：
--
作者：
H. Ichihara
本文研究了具有有界峰值或有界能量扰动的多项式系统的状态反馈综合问题。正不变集由多项式Lyapunov函数的水平集组成，并包含在扰动下的输入区域和状态约束范围内。利用矩阵平方和松弛和半定规划，给出了一种两步非迭代设计方法。第一步，应用矩阵SOS技术。然后，为了消除第一步的保守性原因之一，在第二步中使用了多项式零化子。数值算例说明了所提出的设计方法。
This paper deals with a state feedback synthesis for polynomial systems in the presence of disturbances with bounded peak or bounded energy. Positively invariant sets are composed of level sets of polynomial Lyapunov functions and are included in the region of the inputs and the state constraints under the disturbances. A two-step non-iterative design procedure is available by using matrix sum of squares (SOS) relaxations and semidefinite programming. At the first step, the matrix SOS technique is applied. Then to remove one of the causes of conservativeness of the first step, the polynomial annihilators are utilized in the second step. Numerical examples illustrate the presented design procedure.