ABSTRACT The aim of this paper is to discuss a relaxed observer-based control problem of multiplicative noised Linear Parameter Varying (LPV) systems with unmeasurable states. For discussing the problem, positive definite matrices without neglecting any element are employed to construct a novel parameter-dependent Lyapunov function. Based on the Lyapunov function, some relaxed sufficient conditions are derived to hold the freedom in searching feasible solutions. Furthermore, an extended projective lemma is developed to convert those conditions into Linear Matrix Inequality (LMI) form. Solving these LMI conditions, controller gain and observer gain can be simultaneously obtained in one-step procedure via using convex optimization algorithm. Therefore, an observer-based controller can be established to guarantee the asymptotical stability of the multiplicative noised LPV systems in the sense of mean square. At last, two numerical examples are used to show effectiveness and applicability of the proposed design method.

中文翻译：

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基于扩展投影引理的离散时间乘性噪声 LPV 系统的基于松弛观测器的控制器设计方法

摘要 本文的目的是讨论具有不可测量状态的乘法噪声线性参数变化 (LPV) 系统的基于松弛观测器的控制问题。为了讨论这个问题，使用不忽略任何元素的正定矩阵来构造一个新的依赖于参数的李雅普诺夫函数。基于李雅普诺夫函数，推导出一些宽松的充分条件来保持搜索可行解的自由度。此外，还开发了一个扩展的投影引理来将这些条件转换为线性矩阵不等式 (LMI) 形式。解决这些 LMI 条件，可以通过使用凸优化算法在一步过程中同时获得控制器增益和观测器增益。所以，可以建立一个基于观测器的控制器来保证乘法噪声LPV系统在均方意义上的渐近稳定性。最后，通过两个数值算例说明了所提出的设计方法的有效性和适用性。