scholarly journals Approximation of periodic PDE solutions with anisotropic translation invariant spaces

2017 ◽  
Author(s):  
Ronny Bergmann ◽  
Dennis Merkert
Keyword(s):  
Translation Invariant ◽  
Invariant Spaces ◽  
Translation Invariant Spaces

Translation-invariant spaces of quasianalytic ultradistributions

2015 ◽  
Vol 45 (1) ◽  
pp. 143-175 ◽  
Author(s):  
Bojan Prangoski ◽  
Pavel Dimovski ◽  
Jasson Vindas
Keyword(s):  
Translation Invariant ◽  
Invariant Spaces ◽  
Translation Invariant Spaces

scholarly journals Robust Stability and Stability Radius for Variational Control Systems

2008 ◽  
Vol 2008 ◽  
pp. 1-29 ◽  
Author(s):  
Bogdan Sasu
Keyword(s):  
Control System ◽  
Exponential Stability ◽  
Optimization Techniques ◽  
Stability Radius ◽  
Banach Function Spaces ◽  
Translation Invariant ◽  
Nonautonomous Case ◽  
The Stability ◽  
Invariant Spaces ◽  
Translation Invariant Spaces

We consider an integral variational control system on a Banach spaceXand we study the connections between its uniform exponential stability and the(I(ℝ+,X),O(ℝ+,X))stability, whereIandOare Banach function spaces. We identify the viable classes of input spaces and output spaces related to the exponential stability of systems and provide optimization techniques with respect to the input space. We analyze the robustness of exponential stability in the presence of structured perturbations. We deduce general estimations for the lower bound of the stability radius of a variational control system in terms of input-output operators acting on translation-invariant spaces. We apply the main results at the study of the exponential stability of nonautonomous systems and analyze in the nonautonomous case the robustness of this asymptotic property.

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