A technique of linearizing what we call expectation-based inequality conditions is proposed for control of discrete-time linear systems with stochastic dynamics. In particular, the coefficient random matrices of the systems are assumed to be represented with random polytopes, and the linearization technique is discussed so as to appropriately deal with associated uncertainties. Our expectation-based inequality is an inequality that involves decision variables contained in the expectation operation, and has a unique difficulty in direct linearization, in general. Hence, two key lemmas are provided so that the decision variables can be taken out from the expectation operation. The combinational use of such lemmas and the conventional linear matrix inequality (LMI) techniques, which is nothing but our linearization technique, is expected to be useful for transforming various kinds of expectation-based nonlinear inequality into numerically solvable standard LMIs. As a demonstration, new robust stability conditions are derived with the technique, whose effectiveness is confirmed numerically.

提出了一种将所谓的基于期望的不等式条件线性化的技术，用于控制具有随机动力学的离散时间线性系统。特别地，假设系统的系数随机矩阵由随机多边形表示，并且讨论了线性化技术以便适当地处理相关联的不确定性。基于期望的不等式是一个不等式，它涉及期望操作中包含的决策变量，并且通常在直接线性化方面有独特的困难。因此，提供了两个关键引理，以便可以从期望操作中取出决策变量。此类引理和常规线性矩阵不等式（LMI）技术的结合使用，这不过是我们的线性化技术，有望将各种基于期望的非线性不等式转换为数值可解的标准LMI。作为演示，使用该技术得出了新的鲁棒稳定性条件，其有效性在数值上得到了证实。