分类: 数学 >> 控制和优化 提交时间: 2022-12-12
摘要: In this paper, we study the problem of integral input-to-state stabilization in different norms for parabolic PDEs with integrable inputs. More precisely, we apply the method of backstepping to design a boundary control law for certain linear parabolic PDEs with destabilizing terms and $L^r$-inputs, and establish the integral input-to-state stability in the spatial $L^p$-norm and $W^{1,p}$-norm, respectively, for the closed-loop system, whenever $p in 1,+ infty $ and $r in p,+ infty $. In order to deal with singularities in the case of $p in 1,2)$, we employ the approximative Lyapunov method to analyze the stability in different norms. Concerning with the appearance of external inputs, we apply the method of functional analysis and the theory of series to prove the unique existence and regularity of solution to the closed-loop system.
分类: 动力与电气工程 >> 电气工程 提交时间: 2022-05-29
摘要: 新能源电力系统的动态特性复杂,存在众多稳定分析方法及稳定判据。不同稳定方法/判据对应的物理解释和适用范围不同,目前难以从理论上回答各类判据适合解决的问题,以及它们所对应的物理解释是否合理。该文分为两部分,第一部分提出稳定判据的适用性评估方法,并尝试回答与稳定判据对应的物理解释是否合理;第二部分应用该方法分析部分典型判据的适用场合,并尝试给出其物理解释。第一部分首先回顾归纳现有稳定判据的推演机理,以及各判据背后对应的物理意义。其次,从稳定性等价、标称性和鲁棒性3个角度,提出稳定判据的适用性3个定性原则,并提出基于环路增益灵敏度的定量化指标。最后,以并网变流器为例,说明频域分析中若干基于阻抗的分析方法的性质,并探讨了其适用范围。电力系统中其它典型判据的适用性及其物理解释等工作将在第二部分展开探讨。