Explicit solution of the finite time L2-norm polynomial approximation problem

2011 ◽  
Vol 217 (21) ◽  
pp. 8354-8359 ◽  
Author(s):  
Giuseppe Fedele ◽  
Andrea Ferrise
Keyword(s):  
Polynomial Approximation ◽  
Finite Time ◽  
Explicit Solution ◽  
Approximation Problem ◽  
L2 Norm

L2 norm-based finite-time stability and boundedness of singular distributed parameter systems with parabolic type

2020 ◽  
pp. 095965182096689
Author(s):  
Xingyu Zhou ◽  
Haoping Wang ◽  
Yang Tian
Keyword(s):  
Finite Time ◽  
Sufficient Conditions ◽  
Parabolic Type ◽  
Distributed Parameter Systems ◽  
Temperature Control System ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Stability ◽  
Finite Time Stability ◽  
L2 Norm

In this study, the problem of finite-time stability and boundedness for parabolic singular distributed parameter systems in the sense of [Formula: see text] norm is investigated. First, two new results on [Formula: see text] norm-based finite-time stability and finite-time boundedness for above-mentioned systems, inspired by the light of partial differential equations theory and Lyapunov functional method, are presented. Then, some sufficient conditions of [Formula: see text] norm-based finite-time stability and boundedness are established by virtue of differential inequalities and linear matrix inequalities. Furthermore, the distributed state feedback controllers are constructed to guarantee the [Formula: see text] norm-based finite-time stable and bounded of the closed-loop singular distributed parameter systems. Finally, numerical simulations on a specific numerical example and the building temperature control system equipped with air conditioning are given to demonstrate the validity of the proposed methods.

scholarly journals The general peakon–antipeakon solution for the Camassa–Holm equation

2016 ◽  
Vol 13 (02) ◽  
pp. 353-380 ◽  
Author(s):  
Katrin Grunert ◽  
Helge Holden
Keyword(s):  
Finite Time ◽  
Explicit Solution ◽  
Wave Breaking ◽  
Holm Equation ◽  
Dissipative Case

We compute explicitly the peakon–antipeakon solution of the Camassa–Holm (CH) equation [Formula: see text] in the non-symmetric and [Formula: see text]-dissipative case. The solution experiences wave breaking in finite time, and the explicit solution illuminates the interplay between the various variables.

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