Stabilization of boundary control systems
TLDR
In this paper, a feedback stabilization of a linear hyperbolic boundary value control system is implemented, and the property of controllability of the control system yields the asymptotic stability of the feedback system.About:
This article is published in Journal of Differential Equations.The article was published on 1976-11-01 and is currently open access. It has received 64 citations till now. The article focuses on the topics: Controllability & Boundary value problem.read more
Citations
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Exact controllability and stabilization: The multiplier method
TL;DR: Linear Evolutionary Problems Hidden Regularity Weak Solutions Uniqueness Theorems Exact Controllability Hilbert Uniqueness Method Nonlinear Stabilization Internal Stabilisation of Korteweg-de Vries Equation as discussed by the authors.
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Decay of solutions of wave equations in a bounded region with boundary dissipation
John E. Lagnese,John E. Lagnese +1 more
TL;DR: In this article, an energy decay rate was obtained for solutions of wave type equations in a bounded region in Rn whose boundary consists partly of a nontrapping reflecting surface and partly of an energy absorbing surface.
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Dynamical analysis of distributed parameter tubular reactors
TL;DR: It is shown that these systems are exponentially stable, and that the plug-flow reactor model is observable when the component concentrations are measured at the reactor output and observable with respect to its physical domain when only the product concentration is measured.
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Boundary feedback stabilizability of parabolic equations
TL;DR: In this article, a parabolic equation defined on a bounded domain is considered, with input acting on the boundary expressed as a specified feedback of the solution, and both Dirichlet and mixed (in particular, Neumann) boundary conditions are treated.
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Uniform exponential energy decay of wave equations in a bounded region with L2(0, ∞; L2 (Γ))-feedback control in the Dirichlet boundary conditions
Irena Lasiecka,Roberto Triggiani +1 more
TL;DR: In this paper, an ouvert borne Ω⊂R n, n≥2, on considere l'equation d'onde: W tt =ΔW dans (O,∞)×Ω, avec des conditions initiales W(o,x)=w o (x)∈L 2 (Ω), w 1 (o, x)=w 1(x) ∈H − 1 (ε), and des conditions aux limites non homogenes de type Dirichlet w
References
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Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
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Stability theory for ordinary differential equations.
TL;DR: LaSalle stability theorems refined for ordinary differential equations, discussing classical Liapunov results on system stability were discussed in this article, where they were refined for the case of continuous systems.
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Dynamical systems and stability
TL;DR: Topologies introduced on state space for differential equations to obtain dynamical systems were introduced in this article, where the state space was used to obtain the dynamical system topology of dynamical networks.
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Boundary Control Systems
TL;DR: Boundary conditions control systems described by partial differential equation in domain of Euclidean space analyzed for optimal controllability as discussed by the authors, where the boundary conditions are described by PDEs.