Feedback stabilization for distributed parameter systems of parabolic type, III

1982 ◽  
Vol 31 (1) ◽  
pp. 41-67 ◽  
Author(s):  
Takao Nambu
Keyword(s):  
Parabolic Type ◽  
Distributed Parameter Systems ◽  
Feedback Stabilization ◽  
Distributed Parameter ◽  
Type Iii

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.

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