We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization.Making use of the symmetric positive definite soluti...We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization.Making use of the symmetric positive definite solution of Riccati matrix differential equation which corresponds to the linear time varying control system, we construct the Lyapunov function.Then we provide the sufficent conditions which make that the zero solution of the hyperneutral type nonlinear time varying control systems is uniformly asymptotically stable by means of the Lyapunov equivalence decomposition method, and find the formulaes which can be used to estimate the bounds of the time delays and the nonlinear terms.展开更多
A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an o...A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.展开更多
文摘We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization.Making use of the symmetric positive definite solution of Riccati matrix differential equation which corresponds to the linear time varying control system, we construct the Lyapunov function.Then we provide the sufficent conditions which make that the zero solution of the hyperneutral type nonlinear time varying control systems is uniformly asymptotically stable by means of the Lyapunov equivalence decomposition method, and find the formulaes which can be used to estimate the bounds of the time delays and the nonlinear terms.
基金Project supported by the National Natural Science Foundation of China(Nos.11601517,11502296,61772542,and 61561146395)the Basic Research Foundation of National University of Defense Technology(No.ZDYYJ-CYJ20140101)
文摘A global seventh-order dissipative compact finite-difference scheme is optimized in terms of time stability. The dissipative parameters appearing in the boundary closures are assumed to be different, resulting in an optimization problem with several parameters determined by applying a generic algorithm. The optimized schemes are analyzed carefully from the aspects of the eigenvalue distribution, the ε-pseudospectra, the short time behavior, and the Fourier analysis. Numerical experiments for the Euler equations are used to show the effectiveness of the final recommended scheme.
