ABSTRACT This paper deals with the problem of robust control for a class of discrete time-varying nonlinear stochastic systems with state- and control-dependent noises (also called -dependent noises). In the addressed system, all system parameters are allowed to be time-varying, parameter uncertainties are supposed to be norm-bounded, and nonlinearities are assumed to satisfy the sector-bounded condition. A robust stochastic bounded real lemma is established for the uncontrolled system by means of the Riccati difference equation (RDE). Moreover, a necessary and sufficient condition is presented for the existence of finite-horizon robust control by virtue of the solvability of coupled RDEs, and an iterative algorithm is designed to solve these RDEs. Finally, a numerical example is utilised to illustrate the effectiveness of the derived results.

中文翻译：

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一类具有状态和控制相关噪声的时变非线性随机系统的鲁棒 H2/H∞ 控制

摘要 本文讨论了一类具有状态和控制相关噪声（也称为依赖噪声）的离散时变非线性随机系统的鲁棒控制问题。在寻址系统中，所有系统参数都允许随时间变化，参数不确定性应该是范数有界的，并且假设非线性满足扇区有界条件。通过Riccati差分方程(RDE)为非受控系统建立了一个鲁棒的随机有界实引理。此外，利用耦合RDE的可解性，给出了有限范围鲁棒控制存在的充要条件，并设计了迭代算法来求解这些RDE。最后，通过一个数值例子来说明推导结果的有效性。