This paper focuses on a new state-feedback control synthesis for discrete-time polytopic linear parameter-varying (LPV) systems. The synthesis conditions have been derived using an approach less conservative than those currently found in the literature, which allows to deal with polytopic LPV systems subject to time-varying parameters in all matrices of its state-space representation. Based on parameter-dependent Lyapunov functions, a set of linear matrix inequalities-based conditions is provided to obtain a discrete-time state-feedback controller. Another significant advantage of the proposed conditions is the ability to include the poly-quadratic condition as a particular case, presenting a solution to this so far unresolved problem. In addition, using the same concept, an improved condition for quadratic control synthesis is given. Finally, the effectiveness of the proposed state-feedback control design method is assessed and compared to that of similar approaches by means of numerical examples.

中文翻译：

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多面体LPV系统的离散时间状态反馈控制

本文重点研究离散时间多面体线性参数变化 (LPV) 系统的新状态反馈控制综合。合成条件是使用比目前在文献中发现的方法更不保守的方法得出的，该方法允许处理受其状态空间表示的所有矩阵中的时变参数影响的多面体 LPV 系统。基于参数依赖的李雅普诺夫函数，提供了一组基于线性矩阵不等式的条件来获得离散时间状态反馈控制器。所提出条件的另一个显着优点是能够将多二次条件作为特定情况包括在内，从而为迄今为止尚未解决的问题提供了解决方案。此外，使用相同的概念，二次方程的改进条件给出了控制合成。最后，通过数值例子评估了所提出的状态反馈控制设计方法的有效性，并与类似方法的方法进行了比较。