对带有噪声的随机切换线性系统状态协方差矩阵的界限
Bounding the State Covariance Matrix for a Randomly Switching Linear System with Noise
AI总结：
研究针对随机切换线性系统在噪声下的状态协方差矩阵界限问题，通过Kronecker代数构建扩展系统，提出矩阵优化问题以计算协方差动态的椭球体界限，从而确定切换系统的状态协方差界限。
摘要：
状态向量的传播由一组时间不变的状态转移矩阵控制，这些矩阵在两个值之间任意切换。状态的演化还受到具有随机切换方差的白高斯噪声的扰动。该系统的行为可通过状态向量的协方差矩阵来表征，该矩阵是时间变化的。然而，我们可以通过将切换系统与利用Kronecker代数推导出的扩展系统进行比较，来对协方差集进行界限。我们提出一个矩阵优化问题来计算一个椭球体，该椭球体界定了协方差动态，从而界定了受白噪声影响的切换系统的状态协方差。在开发这一方法的过程中，还计算了线性切换仿射系统的不变椭球体。
英文摘要：
The propagation of a state vector is governed by a set of time-invariant state transition matrices that switch arbitrarily between two values. The evolution of the state is also perturbed by white Gaussian noise with a variance that switches randomly with the state transition relation. The behavior of this system can be characterized by the covariance matrix of the state vector, which is time varying. However, we can bound the set of covariances by comparing the switching system to an augmented system derived with Kronecker algebra. We formulate a matrix optimization problem to compute an ellipsoid that bounds the covariance dynamics, which in turn bounds the state covariance of the set of switching systems subject to white noise. In developing this approach, an invariant ellipsoid for a linear switching affine system is computed along the way.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
