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Exact controllability
results for a multilayer plate system are obtained from the method of Carleman estimates.
The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich
plate” system due to Rao and Nakra. The multilayer version involves a number of
Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation.
The plate is assumed to be either clamped or hinged and controls
are assumed to be locally
distributed in a neighborhood...
Exact controllability
results for a multilayer plate system are obtained from the method of Carleman estimates.
The multilayer plate system is a natural multilayer generalization of a classical three-layer “sandwich
plate” system due to Rao and Nakra. The multilayer version involves a number of
Lamé systems for plane elasticity coupled with a scalar Kirchhoff plate equation.
The plate is assumed to be either clamped or hinged and controls
are assumed to be locally
distributed in a neighborhood...
We consider the problem of boundary control of an elastic system with coupling to a potential equation. The potential equation represents the linearized motions of an incompressible inviscid fluid in a cavity bounded in part by an elastic membrane. Sufficient control is placed on a portion of the elastic membrane to insure that the uncoupled membrane is exactly controllable. The main result is that if the density of the fluid is sufficiently small, then the coupled system is exactly controllable....
The exact internal controllability of the radial solutions of a semilinear heat equation in R3 is proved. The result applies for nonlinearities that are of an order smaller than |s| logp |s| at infinity for 1 ≤ p < 2. The method of the proof combines HUM and a fixed point technique.
We show exact null-controllability for two models of non-classical, parabolic partial differential equations with distributed control: (i) second-order structurally damped equations, except for a limit case, where exact null controllability fails; and (ii) thermo-elastic equations with hinged boundary conditions. In both cases, the problem is solved by duality.
The liner parabolic equation ∂y ∂t − 1 2 Δy + F · ∇ y = 1 x1d4aa; 0 u with Neumann boundary condition on a convex open domain x1d4aa; ⊂ ℝd with smooth boundary is exactly null controllable on each finite interval if 𝒪0is an open subset of x1d4aa; which contains a suitable neighbourhood of the recession cone of x1d4aa; . Here,F : ℝd → ℝd is a bounded, C1-continuous function, and F = ∇g, where g is convex and coercive.
We consider the flow of gas through pipelines controlled by a compressor station. Under a subsonic flow assumption we prove the existence of classical solutions for a given finite time interval. The existence result is used to construct Riemannian feedback laws and to prove a stabilization result for a coupled system of gas pipes with a compressor station. We introduce a Lyapunov function and prove exponential decay with respect to the L2-norm.
We consider the flow of gas through pipelines controlled by a compressor
station. Under a subsonic flow assumption we prove the existence
of classical solutions for a given finite time interval.
The existence result is used to construct Riemannian feedback laws and
to prove a stabilization result for a coupled system of gas pipes with a compressor
station. We introduce a Lyapunov function and prove exponential decay
with respect to the L2-norm.
In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is...
In this paper we study the frequency and
time domain behaviour of a heat exchanger network system.
The system is governed by hyperbolic partial differential
equations. Both the control operator and the observation
operator are unbounded but admissible. Using the theory
of symmetric hyperbolic systems, we prove exponential
stability of the underlying semigroup for the heat exchanger
network. Applying the recent theory of well-posed
infinite-dimensional linear systems, we prove that the
system...
In this paper we study asymptotic behaviour of distributed parameter systems governed by partial differential equations (abbreviated to PDE). We first review some recently developed results on the stability analysis of PDE systems by Lyapunov’s second method. On constructing Lyapunov functionals we prove next an asymptotic exponential stability result for a class of symmetric hyperbolic PDE systems. Then we apply the result to establish exponential stability of various chemical engineering processes...
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