Gain-Scheduling Control System Synthesis Based on Spline-Type Parameter-Dependent Quadratic Forms
Gain-Scheduling Control System Synthesis Based on Spline-Type Parameter-Dependent Quadratic Forms
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基于样条型参数相关二次型的增益调度控制系统综合
DOI：
10.9746/sicetr1965.35.319
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
E. Shimemura
中科院分区：
文献类型：
--
作者：
I. Masubuchi;Ayato Kume;E. Shimemura
本文提出了一种基于样条型参数相关二次型的增益调度控制系统综合方法，该方法保证了系统的稳定性和性能。我们提供了一个程序，以获得一个有限的一组LMI从一个给定的LMI条件的参数依赖二次型。证明了：（1）如果导出的有限LMI集存在解，则它产生一个满足给定LMI条件的可微样条参数依赖二次型。证明了：（2）若存在可微二次型解给定的线性矩阵不等式，则调度参数区域作某种划分的线性矩阵不等式的有限集总是可解的。因此，不同于以往的结果，本文保证了使用计算总是减少保守性求解参数依赖的LMI。这种方法适用于参数依赖的线性矩阵不等式指数稳定性和L2增益性能的分析和综合。
This paper proposes an approach to gain-scheduling control systems synthesis based on spline-type parameter-dependent quadratic forms that guarantee stability and performances of systems. We provide a procedure to derive a finite set of LMIs from a given LMI-condition on a parameter-dependent quadratic form. It is shown that (1) if there exists any solution to the derived finite set of LMIs, it produces a differentiable spline-ty parameter-dependent quadratic form that meets the given LMI-condition. Moreover, we prove that (2) if there exists any differentiable quadratic form solving the given LMI, the finite set of LMIs with some division of scheduling parameter's region is always solvable. Thus unlike previous results this paper guarantees that em-ploying computation always reduce conservatism in solving parameter-dependent LMIs. This approach is applied to parameter-dependent LMIs for analysis and synthesis of exponential stability and L2-gain performance.