This paper addresses the problem of Static Output Feedback (SOF) stabilisation for continuous-time linear systems subject to norm-bounded parameter uncertainties using the Linear Matrix Inequality (LMI) approach. Usually, this issue leads to the feasibility of a Bilinear Matrix Inequality (BMI), which is difficult to linearise to get non-conservative LMI conditions. We present first, in this paper, some background results on the SOF controller design and that are found to be extended to the case of norm-bounded uncertainties. We show that some restrictions on the feasibility of these results should be guaranteed. Moreover, by means of some technical Lemmas, we transform the BMI into a new LMI with a line search over a scalar variable. An enhanced and less conservative LMI condition with a line search over two scalar variables is also developed. Furthermore, a simplified version of each LMI condition without a priori fixed parameters is also presented. An extensive portfolio of numerical examples is presented in order to evaluate the conservativeness and to show the superiority of the proposed design method to the background results.

中文翻译：

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在 LMI 条件下，为受范数有界不确定性影响的连续时间线性系统设计鲁棒静态输出反馈控制器

本文使用线性矩阵不等式 (LMI) 方法解决了受范数有界参数不确定性影响的连续时间线性系统的静态输出反馈 (SOF) 稳定性问题。通常，这个问题会导致双线性矩阵不等式 (BMI) 的可行性，这很难线性化以获得非保守 LMI 条件。我们首先在本文中介绍了 SOF 控制器设计的一些背景结果，这些结果被发现可以扩展到范数有界不确定性的情况。我们表明应该保证对这些结果的可行性的一些限制。此外，通过一些技术引理，我们通过对标量变量的线搜索将 BMI 转换为新的 LMI。还开发了一种增强的、不太保守的 LMI 条件，它对两个标量变量进行线搜索。此外，还介绍了没有先验固定参数的每个 LMI 条件的简化版本。提供了广泛的数值示例组合，以评估保守性并展示所提出的设计方法对背景结果的优越性。