scholarly journals Large Time Stability Control for a Class of Quasilinear Parabolic and Hyperbolic Equations

2017 ◽  
Author(s):  
Hongen Li ◽  
SHuxian Deng
Keyword(s):  
Large Time ◽  
Hyperbolic Equations ◽  
Stability Control ◽  
Time Stability ◽  
Quasilinear Parabolic

scholarly journals Krylov SSP Integrating Factor Runge–Kutta WENO Methods

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1483
Author(s):  
Shanqin Chen
Keyword(s):  
Large Time ◽  
Hyperbolic Equations ◽  
Strong Stability ◽  
Matrix Exponential ◽  
Linear Component ◽  
Nonlinear Hyperbolic Equations ◽  
Time Step ◽  
Integrating Factor ◽  
The Matrix ◽  
Runge Kutta

Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) problems by a splitting method. How to evaluate the matrix exponential operator efficiently is a tremendous challenge when we apply IF temporal discretization for PDEs on high spatial dimensions. In this work, the matrix exponential computation is approximated through the Krylov subspace projection method. Numerical examples are shown to demonstrate the accuracy and large time-step size of the present method.

scholarly journals Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Maoxing Liu ◽  
Jie Wu ◽  
Yong-zheng Sun
Keyword(s):  
Stability Analysis ◽  
Permanent Magnet ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Stability Control ◽  
Time Stability ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Comparison Results

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

Boundary effects and large-time behaviour for quasilinear equations with nonlinear damping

2015 ◽  
Vol 145 (5) ◽  
pp. 959-978 ◽  
Author(s):  
Shifeng Geng ◽  
Lina Zhang
Keyword(s):  
Asymptotic Behaviour ◽  
Large Time ◽  
Convergence Rates ◽  
Hyperbolic Equations ◽  
Nonlinear Damping ◽  
Boundary Effects ◽  
Time Behaviour ◽  
Quasilinear Equations ◽  
Quasilinear Hyperbolic Equations ◽  
Quarter Plane

This paper is concerned with the asymptotic behaviour of solutions to quasilinear hyperbolic equations with nonlinear damping on the quarter-plane (x, t) ∈ ℝ+ x ∈ ℝ+. We obtain the Lp (1 ≤ p ≤ +∞) convergence rates of the solution to the quasilinear hyperbolic equations without the additional technical assumptions for the nonlinear damping f(v) given by Li and Saxton.

scholarly journals A Riccati solution for the ideal MHD plasma response with applications to real-time stability control

2018 ◽  
Vol 25 (3) ◽  
pp. 032507 ◽  
Author(s):  
Alexander S. Glasser ◽  
Egemen Kolemen ◽  
A. H. Glasser
Keyword(s):  
Real Time ◽  
Stability Control ◽  
Time Stability ◽  
Ideal Mhd ◽  
Plasma Response ◽  
The Ideal ◽  
Real Time Stability

scholarly journals Robust H∞ finite-time stability control of a class of nonlinear systems

2016 ◽  
Vol 40 (7-8) ◽  
pp. 5111-5122 ◽  
Author(s):  
Haitao Liu ◽  
Xuehong Tian ◽  
Gui Wang ◽  
Tie Zhang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Stability Control ◽  
Time Stability ◽  
Finite Time Stability
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