In this paper, for continuous, linearly-controllable quadratic controlsystems with a single input, an explicit, constructive method is proposed forstudying their Brunovsky forms, initially studied in [W. Kang and A. J. Krener,Extended quadratic controller normal form and dynamic state feedbacklinearization of nonlinear systems, SIAM Journal on Control and Optimization,30:1319-1337, 1992]. In this approach, the computation of Brunovsky forms andtransformation matrices and the proof of their existence and uniqueness arecarried out simultaneously. In addition, it is shown that quadratictransformations in the aforementioned paper can be simplified to preventmultiplicity in Brunovsky forms. This method is extended for studying discretequadratic systems. Finally, computation algorithms for both continuous anddiscrete systems are summarized, and examples demonstrated.
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机译：在本文中，对于具有单个输入的连续，线性可控的二次控制系统，提出了一种明确的构造方法来研究其Brunovsky形式，该方法最初在[W. Kang和A. J. Krener，非线性系统的扩展二次控制器正规形式和动态状态反馈线性化，SIAM，控制与优化杂志，30：1319-1337，1992]。该方法同时进行了布鲁诺夫斯基形式和变换矩阵的计算以及它们存在和唯一性的证明。另外，表明可以简化前述论文中的二次变换以防止布鲁诺夫斯基形式的多重性。该方法被扩展用于研究离散二次系统。最后，总结了连续和离散系统的计算算法，并举例说明。
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