Approaches to robust ℋ︁∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties
Approaches to robust ℋ︁∞ static output feedback control of discrete‐time piecewise‐affine systems with norm‐bounded uncertainties
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DOI：
10.1002/rnc.1627
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发表时间：
2011-05
影响因子：
3.9
通讯作者：
Jianbin Qiu;G. Feng;Huijun Gao
中科院分区：
文献类型：
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作者：
Jianbin Qiu;G. Feng;Huijun Gao
研究了一类具有范数有界时变参数不确定性的离散分段仿射系统的鲁棒ℋ︁∞静态输出反馈控制器设计问题。目标是设计一种分段线性静态输出反馈控制器，保证闭环系统在给定的ℋ︁∞干扰抑制水平下渐近稳定。基于分段李雅普诺夫函数，结合S过程、投影引理和一些矩阵不等式凸化技术，提出了几种分析和综合分段仿射系统静态输出反馈控制器的新方法。结果表明，控制器的增益可以通过求解一组严格的线性矩阵不等式(LMI)或由一个或两个标量变量参数化的一族LMI来获得，这在商业软件中是数值有效的。最后，给出了三个仿真实例，验证了所提方法的有效性。版权所有©2010 John Wiley&Sons，Ltd.
This paper investigates the problem of robust ℋ︁∞ static output feedback controller design for a class of discrete‐time piecewise‐affine systems with norm‐bounded time‐varying parametric uncertainties. The objective is to design a piecewise‐linear static output feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop system with a prescribed ℋ︁∞ disturbance attenuation level. Based on a piecewise Lyapunov function combined with S‐procedure, Projection lemma, and some matrix inequality convexifying techniques, several novel approaches to the static output feedback controller analysis and synthesis are developed for the underlying piecewise‐affine systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities (LMIs) or a family of LMIs parameterized by one or two scalar variables, which are numerically efficient with commercially available software. Finally, three simulation examples are provided to illustrate the effectiveness of the proposed approaches. Copyright © 2010 John Wiley & Sons, Ltd.