Abstract

We consider a linear discrete time-varying system with multiplicative noise acted upon by colored exogenous disturbance with nonzero first moment. Multiplicative noises are modeled in the form of linear combinations of deterministic matrices with pairwise independent random coefficients. For this system, we describe a method, based on a state-space realization, for calculating the anisotropic norm in terms of Riccati equations.

中文翻译：

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非中心扰动下具有乘性噪声系统的各向异性范数有界性的引理

摘要

我们考虑一个线性离散时变系统，该系统具有乘性噪声，该噪声受有色外源性扰动作用，且第一矩不为零。以确定性矩阵与成对独立的随机系数的线性组合形式对乘性噪声建模。对于该系统，我们描述了一种基于状态空间实现的，根据Riccati方程计算各向异性范数的方法。