State space realizations robust to overloading for discrete-time LTI systems
State space realizations robust to overloading for discrete-time LTI systems
复制标题
离散时间 LTI 系统的状态空间实现对过载具有鲁棒性
DOI：
10.1016/j.sigpro.2018.10.017
复制
发表时间：
2019
影响因子：
4.4
通讯作者：
Yoshimura Yuichi
中科院分区：
文献类型：
--
作者：
Ohno Shuichi;Yoshimura Yuichi
在数字信号处理中，如果信号的幅度超过预定限制，则会发生值过载。应该避免超载，因为它可能会对系统造成灾难性的影响。为了缓解超载，多年来一直使用2范数标度。然而，2范数定标并不总是有效的，因为它与信号的幅度没有直接关系。本文提出了一种对过载具有鲁棒性的数字离散时间LTI系统的状态空间实现设计方法。利用不变集理论求出了状态变量幅值的上界。当分配不同的位数来表示状态变量的值时，我们的实现是通过最小化椭球不变量集的体积来给出的。另一方面，当为每个状态变量分配相同数量的比特时，状态变量的大小的上界被最小化，并且通过球面不变量集获得最优实现。数值算例表明，我们的实现对过载具有较强的鲁棒性。
In digital signal processing, overloading of a value occurs if the amplitude of a signal exceeds a predetermined limit. The overloading should be avoided, since it may cause a catastrophic effect on the system. To mitigate the overloading, thel2norm scaling has been utilized for many years. However, thel2norm scaling does not always work well, since it is not directly related to the amplitude of the signal. This paper presents a design method of state space realizations for digital discrete-time LTI systems that are robust to overloading. Upper bounds of the amplitudes of state variables are evaluated by using the invariant set theory. When different numbers of bits are allocated to represent the values of state variables, our realization is given by minimizing the volume of an ellipsoidal invariant set. On the other hand, when an equal number of bits is assigned to each state variable, an upper bound on the magnitude of the state variables is minimized and the optimal realization is obtained by the spherical invariant set. Numerical examples are provided to show that our realizations are robust to overloading.