Partial Stability for a Class of Nonlinear Systems
Partial Stability for a Class of Nonlinear Systems
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一类非线性系统的部分稳定性
DOI：
10.1137/070708421
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发表时间：
2009
影响因子：
2.2
通讯作者：
Costa E
中科院分区：
文献类型：
--
作者：
Costa E
本文研究了卡尔曼滤波器稳定性分析中出现的一个非线性离散矩阵系统。这些系统呈现出状态组件之间的内部耦合，从而产生复杂的动态行为。研究并解决了要求系统某一特定状态分量指数收敛的部分稳定问题。收敛状态分量与卡尔曼滤波器的行为密切相关，因为它可以用来为噪声测量中不确定情况下的误差协方差矩阵提供边界。利用系统的特殊性质，主要是与线性系统的联系，得到了系统部分稳定性的代数检验。最后，在可接受估计多项式散度的应用中，我们研究并解决了一个部分半稳定性问题。
This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system—mainly the connections with linear systems—to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.