Incremental input-to-state stability for Lur'e systems and asymptotic behaviour in the presence of Stepanov almost periodic forcing

2021 ◽  
Vol 300 ◽  
pp. 692-733
Author(s):  
Max E. Gilmore ◽  
Chris Guiver ◽  
Hartmut Logemann
Keyword(s):  
Asymptotic Behaviour ◽  
Almost Periodic ◽  
Periodic Forcing ◽  
Lur’E Systems

scholarly journals Escaping Orbits Are also Rare in the Almost Periodic Fermi–Ulam Ping-Pong

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Henrik Schließauf
Keyword(s):  
Lebesgue Measure ◽  
Measure Zero ◽  
Initial Condition ◽  
Almost Periodic ◽  
Periodic Forcing ◽  
One Dimensional ◽  
Forcing Function ◽  
Ping Pong ◽  
The One ◽  
Escaping Orbits

AbstractWe study the one-dimensional Fermi–Ulam ping-pong problem with a Bohr almost periodic forcing function and show that the set of initial condition leading to escaping orbits typically has Lebesgue measure zero.

Almost-periodic forcing for a wave equation with a nonlinear, local damping term

1983 ◽  
Vol 94 (3-4) ◽  
pp. 195-212 ◽  
Author(s):  
Alain Haraux
Keyword(s):  
Maximal Monotone ◽  
Nonlinear Hyperbolic Equation ◽  
List Type ◽  
Almost Periodic ◽  
Damping Term ◽  
Periodic Forcing ◽  
Maximal Monotone Graph ◽  
Image Position ◽  
Uniformly Continuous ◽  
Monotone Graph

SynopsisLet Ω⊂ℝnbe a bounded open domain and T = ∂Ω. It β is a maximal monotone graph in ℝ×ℝ with 0ϵβ(0), and f: ℝ×Ω→ℝ is measurable with t→ f(t,.) S2-almost periodic as a function ℝ→L2(Ω), we consider the nonlinear hyperbolic equationWe show that:(i) if ゲ is strictly increasing and (1) has a solution ω on ℝ with [ω, Əω/Ət] almost periodic: , for any solution of (1) there exists with u(t,.)–ω(t,.)—ξin (ii) if β is single valued and everywhere defined, the existence of ω as above implies that, for every solution of (1), there exists Ϛ(t, x) with ә2Ϛ/әt2–0△Ϛ = in ℝ×Ω and u(t,.)–ω(t,.)—0 in as t → +∞(iii) if β–1 is uniformly continuous and ゲ satisfies some growth assumption (depending on N), for every f as above, there exists ω solution of (1) on ℝ with [ω, Əω/Ət] almost periodic: ℝ → .

Sign in / Sign up

Export Citation Format

Share Document