Subjects: Mathematics >> Control and Optimization. submitted time 2022-12-12
Abstract：
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.
Peer Review Status:
Awaiting Review
Subjects: Dynamic and Electric Engineering >> Electrical Engineering submitted time 2022-05-29
Abstract：
Many methods and criteria of stability assessment have been proposed due to the complex dynamics of renewable power system. The physical implications of these methods/criteria and their scopes of adaptation are different. It is difficult to theoretically answer that, for certain stability issue, which stability criterion is suitable and whether the corresponding physical interpretation is reasonable. This paper was divided into two parts. The methods for assessing the adaptation of stability criteria were put forward, and the question whether the corresponding physical interpretations were reasonable were answered in part I. While the adaptation of each stability criterion was analyzed by applying the method and the physical interpretation of each stability problem was derived in part II. In part I, the derivation process of the existing stability criteria and their underlying physical significance were reviewed at first. Secondly, the selection principles of stability criteria were proposed from 3 aspects, namely stability equivalence, nominal performance and robust stability. And the quantitative index named loop gain sensitivity was proposed. Finally, the adaptation of several impedance criteria of grid-connected converters were analyzed.?It was shown that the nominal performance and robustness of these impedance criteria were not equivalent in frequency domain modal analysis. The adaptation of other typical stability criteria and the corresponding physical interpretation were analyzed in part II.
" "
Peer Review Status:Awaiting Review
Hits
Hits
Downloads
Comment