A Unified Algebraic Approach to Linear Control Design, R.E. Skelton, T. Iwasaki and K. Grigoriadis, Taylor & Francis, London, UK, 1998, 285 pages. ISBN 0‐7484‐0592‐5
A Unified Algebraic Approach to Linear Control Design, R.E. Skelton, T. Iwasaki and K. Grigoriadis, Taylor & Francis, London, UK, 1998, 285 pages. ISBN 0‐7484‐0592‐5
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线性控制设计的统一代数方法，R.E. Skelton、T. Iwasaki 和 K. Grigoriadis，Taylor & Francis，英国伦敦，1998 年，ISBN 0‐7484‐0592‐5。
DOI：
10.1002/rnc.694
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
V. Balakrishnan
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文献类型：
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作者：
V. Balakrishnan
可以说，无论是从经典频域方法的角度，还是从现代状态空间方法的角度，有限维线性系统理论都是一个研究得很好、理解得很好的话题。这就引出了一个问题，即20世纪90年代末出版的一本关于线性控制设计的书能增加什么。事实证明，相当多。世纪后半叶线性系统理论的许多进展都是在状态空间环境中取得的。突出的例子是20世纪60年代提出的LQG控制器[1]和20世纪80年代导出的H1控制器[2]。这两个主要发展的基础是一定的二次李雅普诺夫函数的概念，“证明”的控制器设计的最优性。在1980年代末和1990年代初，一般控制系统的李雅普诺夫函数的数值搜索技术得到了发展。对于各种各样的控制系统模型，二次李雅普诺夫函数的搜索减少到线性矩阵不等式（LMI）的可行性。这一观察是在核心的书'线性矩阵不等式在系统和控制理论'，由博伊德等人。[3]的文件。对于有限维线性时不变（LTI）系统，通常的情况是，如果存在证明某个性质的李雅普诺夫函数，则二次李雅普诺夫函数也存在。然后，在LTI控制理论中的一些“经典”问题，可以重新审视在搜索二次李雅普诺夫函数的上下文中。许多研究人员已经进行了这方面的研究和相关的研究;参考文献[4-9]提供了一个代表性但不完整的列表。
It is fair to say that finite-dimensional linear system theory is a well-studied and well-understood topic, be it from the angle of the classical frequency-domain-based methods, or from the viewpoint of the modern state-space methods. This begs the question of what can be added by a book on linear control design published in the late 1990s. Quite a lot, it turns out. Many of the advances in linear system theory in the latter half of the 20th century have come in a state-space setting. Prominent examples are the LQG controller proposed in the 1960s [1], and the H1 controller derived in the 1980s [2]. Underlying both these major developments is the notion of a certain quadratic Lyapunov function that ‘proves’ the optimality of the controller designed. In the late 1980s and the early 1990s, techniques were developed for the numerical search for Lyapunov functions for general control systems. For a wide variety of control system models, the search for quadratic Lyapunov functions reduces to the feasibility of linear matrix inequalities (LMIs). This observation was at the heart of the book ‘Linear Matrix Inequalities in System and Control Theory’, by Boyd et al.[3]. For finite-dimensional linear time-invariant (LTI) systems, it is usually the case that if a Lyapunov function exists that proves a certain property, a quadratic Lyapunov function also exists. Then, a number of ‘classical’problems in LTI control theory can be revisited in the context of a search for quadratic Lyapunov functions. A number of researchers have pursued this and related lines of research; a representative but incomplete list is provided by References [4–9].