Hautus–Yamamoto criteria for approximate and exact controllability of linear difference delay equations

A ug 2 01 7 Approximate and exact controllability of linear difference equations ∗

In this paper, we study approximate and exact controllability of the linear difference equation x(t) = ∑Nj=1A jx(t −Λ j) +Bu(t) in L2, with x(t) ∈ C and u(t) ∈ C, using as a basic tool a representation formula for its solution in terms of the initial condition, the control u, and some suitable matrix coefficients. When Λ1, . . . ,ΛN are commensurable, approximate and exact controllability are e...

Approximate Boundary Controllability for Semilinear Delay Differential Equations

Approximate Controllability for Linear Stochastic Differential Equations in Infinite Dimensions

The objective of the paper is to investigate the approximate controllability property of a linear stochastic control system with values in a separable real Hilbert space. In a first step we prove the existence and uniqueness for the solution of the dual linear backward stochastic differential equation. This equation has the particularity that in addition to an unbounded operator acting on the Y...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Exact and Approximate Sparse Solutions of Underdetermined Linear Equations

In this paper, we empirically investigate the NP-hard problem of finding sparsest solutions to linear equation systems, i.e., solutions with as few nonzeros as possible. This problem has received considerable interest in the sparse approximation and signal processing literature, recently. We use a branch-and-cut approach via the maximum feasible subsystem problem to compute optimal solutions fo...