On the relation between analysis and synthesis conditions for discrete-time systems with saturation nonlinearities
On the relation between analysis and synthesis conditions for discrete-time systems with saturation nonlinearities
复制标题
具有饱和非线性的离散时间系统的分析与综合条件的关系
DOI：
10.1109/cdc.2005.1583477
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
K. Sawada
中科院分区：
文献类型：
--
作者：
T. Kiyama;K. Sawada
本文考虑了具有饱和和/或死区非线性的线性时不变（LTI）离散系统，提出了基于二次Lyapunov函数的区域性能和/或极点配置的分析和综合方法，该方法采用广义扇形和多面体方法。特别地，一个新的l2performance域是由考虑l2performance和/或极点位置的系统初始状态区域定义的。通过分析，基于这两种方法的问题可以分别转化为线性矩阵不等式（LMI）优化问题，并证明了在单一饱和或单一死区非线性的特殊情况下，广义扇形方法与多面体方法完全相同。同样，对于综合，基于广义扇形方法的问题可以被重新定义为LMI优化问题，其中非线性的输出被假设为可用于控制。其次，澄清了两者之间的关系，即当采样周期趋于零时，分析和综合条件可以简化为连续时间系统的相应条件。最后，通过一个数值算例指出了基于lmi的方法对设计防卷绕控制系统的帮助。
This paper considers linear time-invariant (LTI) discrete-time systems with saturation and/or dead-zone nonlinearities, and proposes analysis and synthesis methods of a regional l2performance and/or a pole placement based on a quadratic Lyapunov function via a generalized sector and a polytopic approach. In particular, a new domain of l2performance is defined by a region of initial states of the system considering the l2performance and/or the pole placement. For analysis, the problems based on the two approaches can be recast as linear matrix inequality (LMI) optimization ones respectively, and in the special case of single saturation or single dead-zone nonlinearity, it is proved that the generalized sector approach is exactly the same as the polytopic approach. Similarly, for synthesis, the problem based on the generalized sector approach can be recast as an LMI optimization problem where the outputs of the nonlinearities are assumed to be available for control. Next, the relation is clarified that the analysis and synthesis conditions can be reduced to the corresponding conditions for the continuous-time systems as the sampling period goes to zero. Finally, it is pointed out that our LMI-based approach is helpful through a numerical example designing anti-windup control systems.