具有概率输入时滞系统的随机耗散性
Stochastic Dissipativity for Systems with Probabilistic Input Delays
AI总结：
针对概率输入时滞系统，从算子理论定义随机耗散性与稳定性，推广开环条件，导出非线性准则及LMI条件，数值实验显示比确定性方法保守性更低。
摘要：
这项工作考虑了一般内积空间中的随机算子，特别是具有已知概率分布的随机时变输入时滞的系统。从算子理论的角度定义了随机耗散性和稳定性，并将众所周知的用于闭环/网络稳定性的开环耗散性条件推广到随机情形。推导了识别具有随机输入时滞的耗散非线性系统的准则，并利用该结果找到了具有已知概率分布输入时滞的线性系统随机耗散性的时滞分布相关线性矩阵不等式条件。数值实验证明了所得准则在鲁棒对象分析和控制器设计中的实用性，突出了与确定性方法相比显著降低的保守性。
英文摘要：
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from an operator-theoretic perspective, and the well-known open-loop dissipativity conditions for closed-loop/network stability are extended to the stochastic case. Criteria are derived to identify dissipative nonlinear systems with stochastic input delays, and this result is used to find delay-distribution-dependent linear matrix inequality conditions for stochastic dissipativity of a linear system with input delays of a known probability distribution. A numerical experiment demonstrates the utility of the resulting criteria for robust plant analysis and controller design, highlighting significantly reduced conservatism compared to deterministic methods.
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