ABSTRACT We revisit the issue of quadratic gain-scheduled and robust state-feedback control with a focus on linear matrix inequalities widely used in the literature. It has been established that for continuous-time linear parameter-varying systems which depend affinely on the scheduling parameter, gain-scheduled stabilisability implies robust stabilisability. In other words, as far as stabilisation is concerned, using a more complex gain-scheduled controller is not advantageous. The proof of such equivalence is non constructive and, although very general, limited to stabilisability. One contribution of the present paper is to establish constructive proofs in the quadratic case that can be extended to performance optimisation in terms of quadratic and norms. One issue investigated in detail is the strategy of using pre-filters to handle parameter-variation in the input matrix. Our results show that said technique, which has been popular since the 1980s, is rarely productive in the sense that solvability of quadratic gain-scheduled control design problems for the original system augmented with an arbitrary pre-filter implies existence of a lower-dimensional quadratic robust controller for the original system, which we construct explicitly via projections.

中文翻译：

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连续时间二次增益调度和鲁棒状态反馈控制中的预滤波

摘要 我们重新讨论了二次增益调度和鲁棒状态反馈控制的问题，重点是在文献中广泛使用的线性矩阵不等式。已经确定，对于仿射依赖于调度参数的连续时间线性参数变化系统，增益调度的稳定性意味着稳健的稳定性。换句话说，就稳定性而言，使用更复杂的增益调度控制器并不有利。这种等价的证明是非建设性的，虽然非常笼统，但仅限于稳定性。本文的一个贡献是在二次情况下建立构造性证明，可以扩展到二次和范数方面的性能优化。详细研究的一个问题是使用预过滤器处理输入矩阵中的参数变化的策略。我们的结果表明，自 1980 年代以来一直流行的所述技术很少有成效，因为原始系统的二次增益调度控制设计问题的可解性暗示存在低维二次原始系统的鲁棒控制器，我们通过投影明确构建。