Infinite dimensional Lyapunov equation
Integral Quadratic Constraints on Linear Infinite-dimensional Systems for Robust Stability Analysis
... an infinite-dimensional uncertainty (Barreau et ...an infinite-dimensional type of uncer- tainties modeled by a linear Partial Differential ...the Lyapunov-Krasovskii theorem and ...
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Lyapunov stability analysis of a string equation coupled with an ordinary differential system
... finite dimensional dynamic control law generated by an ODE [8] or on the contrary the robustness of a linear closed loop system with a control signal conveyed by a damped string ...an infinite ...
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On Galerkin Method for Homogeneous Infinite-Dimensional Systems
... original infinite-dimensional evolution ...Burgers equation confirm a large improvement of the estimation precision of the ho- mogeneous Galerkin projection in comparison with the classical Galerkin ...
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Lyapunov stability analysis of a linear system coupled to a heat equation
... 6. DISCUSSION AND CONCLUSION In this paper, we have provided a novel approach to assess stability of coupled ODE-Heat PDE systems. The method relies on an efficient construction of dedicated Lya- punov functionals ...
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Integral and measure-turnpike properties for infinite-dimensional optimal control systems
... turnpike property holds or not for the adjoint state λ T . As mentioned above, having such a result is particularly important in view of numerical issues. Local versus global properties. It is interesting to stress on ...
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Hilbert and Thompson geometries isometric to infinite-dimensional Banach spaces
... ball, infinite outside the dual ball, and weak* lower semi-continuous, and has infimum ...finite dimensional spaces, but the proof works in infinite dimension as ...
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Boundary maps and maximal representations on infinite dimensional Hermitian symmetric spaces
... our infinite dimensional setting, we use the same space I p of isotropic linear subspaces of dimension ...this infinite dimensional context: this space is not com- pact anymore for the natural ...
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A CLT Plancherel representations of the infinite-dimensional unitary group
... The same limiting object (the collection of correlated GFFs) has been pre- viously shown to be the universal global scaling limit for eigenvalues of various submatrices of Wigner Hermitian random matrices, cf. [2]. We ...
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Infinite-dimensional regularization of McKean-Vlasov equation with a Wasserstein diffusion
... dX t = (AX t + B(X t ))dt + dW t , (3) for a certain class of self-adjoint, negative definite operators A : D(A) ⊂ H → H, for W a cylindrical Wiener process on H and for B : H → H only measurable and locally bounded. For ...
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An application of the Malliavin calculus to infinite dimensional diffusions
... Diffusions on the infinite product of a compact manifold are defined, and their finite dimensional marginals studied.. It is shown that under reasonable.[r] ...
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Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies
... When the preferred sets and/or the aggregate production set are nonconvex, it is not always possible to find prices for which consumer and producer choices at a Pareto optimal allocation are truly optimal. An equilibrium ...
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INFINITE DIMENSIONAL MULTIPLIERS AND PONTRYAGIN PRINCIPLES FOR DISCRETE-TIME PROBLEMS
... (4) hλ 0 .D 2 φ t (ˆ x t , u ˆ t ) + p t+1 ◦ D 2 f t (ˆ x t , u ˆ t ), u t − ˆ u t i ≤ 0 for all t ∈ N and for all u t ∈ U t . The proofs of Theorem 2.2 and Theorem 2.3 are based on the following two ideas: the first ...
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Algebraic damping in the one-dimensional Vlasov equation
... Euler equation, as well as other related conservative 2D fluid equations, share a lot of similarities with the Vlasov ...Vlasov equation, linearized around a non homogeneous stationary state, one would ...
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LIMITING MOTION FOR THE PARABOLIC GINZBURG-LANDAU EQUATION WITH INFINITE ENERGY DATA
... • a localizing property for the energy inspired by Lin and Rivière [27] • refined Jacobian estimates due to Jerrard and Soner [23] • techniques first developed for the stationary equation (for example [4, 5, 6]). ...
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The Lojasiewicz gradient inequality in the infinite dimensional Hilbert space framework
... In order to prove (7) it suffices to apply Lemma 5.2 with W = V ′ , F = R(A), N = ker A ⊂ V ⊂ V ′ , n = Πu, f = Au, n + f = Lu. Indeed we have ∀u ∈ V, kuk V ≤ ku − Πuk V + kΠuk V ≤ ρ −1 kA(u − Πu)k V ′ + KkΠuk V ′ by ...
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Distance estimates for state constrained trajectories of infinite dimensional differential inclusions
... ∂ t u ∈ ∆u + F (t, u) in (0, 1) × Ω ∂ t u = −∂ ν u − γu on (0, 1) × ∂Ω. Here u = u(t, x), Ω is a bounded domain of R N with smooth boundary and γ ∈ C(∂Ω). This kind of systems has been the object of an intense research, ...
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Applications of probability to partial differential equations and infinite dimensional analysis
... We first review the results in finite dimensional spaces, and then examine the infinite dimensional analog under Gaussian measures.. The various techniques developed [r] ...
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An application of the Bakry-Emery criterion to infinite dimensional diffusions
... We begin by recalling their criterion in the setting with which we will be dealing.. However, the refinement seems to become less and less significant as N becomes lar[r] ...
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Duality in RKHSs with Infinite Dimensional Outputs: Application to Robust Losses
... 5. Conclusion This work presents a versatile framework based on duality to learn OVK machines with infinite dimensional outputs. The case of convolved losses (e.g. -insensitive, Huber) is thoroughly ...
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Identification of dielectric relaxations: a suitable infinite-dimensional state-space approach
... associated to dielectric viscosity. When the involved dynamic operators are of rational type, classical state space formulations are efficiently and widely used in commercial simulators (Matlab-Simulink, Pspice etc.). In ...
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