Stability of bilinear time-delay systems
Stability of bilinear time-delay systems
复制标题
双线性时滞系统的稳定性
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
Song Wenzhong
中科院分区：
文献类型：
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作者：
Jiang Guojun;Song Wenzhong
双线性系统是非线性系统的一个重要子类。双线性表示已经在各种工程领域被发现：例如，参见Koivo & Cojocariu (1977)；Espana & Landau（1978）。近年来，人们开始关注双线性系统的稳定性（Quinn, 1980; Longchamp, 1980; young et al., 1989）。大多数论文考虑具有线性反馈的时不变连续双线性系统。几乎所有的文献都通过寻找反馈控制存在的充分条件来研究稳定性，从而使闭环系统渐近稳定。在一些众所周知的结果中，稳定性的充分条件要求系统存在Liapunov函数或存在一些负（或正）定矩阵，使得反馈输入u(t)依赖于这些矩阵，但有时这些矩阵不容易找到。在实际情况下，大多数系统都会受到时延因素的影响。时滞系统在理论和应用上都是研究的难点。即使对于一阶定系统，由于解空间的无限大维数，讨论解和性质也是困难的。本文首先研究了微分双线性时滞系统的稳定性。给出了一些有意义的结果。研究了连续时间情况下具有输出反馈的时变双线性时滞系统。这里我们假设反馈函数f在一个包含满足Lipschitz条件的线性函数和二次函数的函数空间中。采用归一变换方法进行分析，见季国军、宋文忠（1997）。
Bilinear systems are an important subclass of nonlinear systems. Bilinear representations have been found in various engineering areas: see, for example Koivo & Cojocariu (1977); Espana & Landau (1978). Recently, attention has been given to the stability of bilinear systems (Quinn, 1980; Longchamp, 1980; Youg et al., 1989). Most papers consider timeinvariant continuous bilinear systems with linear feedback. Almost all of the references study stability by finding a sufficient condition for the existence of a feedback control such that the resulting closed-loop system is asymptotically stable. In some well known results, the sufficient conditions for stability require the existence of Liapunov functions for the systems or the existence of some negation (or positive) definite matrices such that the feedback input u(t) depends on those matrices, but sometimes those matrices are not easy to find. Most systems are influenced by time-delay factors in practical circumstances. Timedelay systems are difficult to study both in theory and application. Even for first-order definite systems, discussion of solutions and properties is difficult because of the infinite dimension in solutions space. In this paper, the stability of the differential bilinear time-delay system is first studied. Some significant results are given. We consider the time-varying bilinear time-delay systems with output feedback in the continuous-time case. Here we assume that the feedback function f is in a function space which includes linear functions, these satisfying the Lipschitz conditions and quadratic functions. The analysis is given using the normtransformation method, see Ji Guojun & Song Wenzhong (1997).