scholarly journals Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays

2016 ◽  
Vol 26 (2) ◽  
pp. 189-197 ◽  
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Multiple Time ◽  
Multiple Time Delays

Abstract Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived.

scholarly journals Pointwise observation of the state given by complex time lag parabolic system

2017 ◽  
Vol 27 (1) ◽  
pp. 77-89
Author(s):  
Adam Kowalewski
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Neumann Boundary Condition ◽  
Optimization Problems ◽  
Time Lag ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
The State ◽  
Constant Time ◽  
Time Lags

AbstractVarious optimization problems for linear parabolic systems with multiple constant time lags are considered. In this paper, we consider an optimal distributed control problem for a linear complex parabolic system in which different multiple constant time lags appear both in the state equation and in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic time lag equation with the Neumann boundary condition are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional with pointwise observation of the state and constrained control are derived. The example of application is also provided.

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

Robust stability of uncertain linear systems with multiple time delays

1997 ◽  
Vol 211 (3) ◽  
pp. 195-202
Author(s):  
Y Fang
Keyword(s):  
Linear Systems ◽  
Robust Stability ◽  
Time Delays ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Multiple Time ◽  
Time Delay Systems ◽  
Multiple Time Delays ◽  
Uncertain Linear Systems

In this paper, the robust stability of uncertain linear systems with multiple time delays is studied. Sufficient conditions for robust stability of linear time delay systems with convex perturbations are obtained. From these sufficient conditions, a few results on robust stability of systems with other perturbations are derived. Some previously known sufficient conditions are generalized.

scholarly journals Optimality Conditions for Infinite Order Distributed Parabolic Systems with Multiple Time Delays Given in Integral Form

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Bahaa G. M.
Keyword(s):  
Optimality Conditions ◽  
Time Delays ◽  
Infinite Order ◽  
Neumann Boundary ◽  
Integral Form ◽  
Parabolic Systems ◽  
Multiple Time ◽  
State Equations ◽  
Multiple Time Delays ◽  
Performance Functional

The optimal boundary control problem for (n×n) infinite order distributed parabolic systems with multiple time delays given in the integral form both in the state equations and in the Neumann boundary conditions is considered. Constraints on controls are imposed. Necessary and suffacient optimality conditions for the Neumann problem with the quadratic performance functional are derived.

Stability and Instability of the Wave Equation Solutions in a Pulsating Domain

1998 ◽  
Vol 10 (07) ◽  
pp. 925-962 ◽  
Author(s):  
J. Dittrich ◽  
P. Duclos ◽  
N. Gonzalez
Keyword(s):  
Boundary Condition ◽  
Neumann Boundary Condition ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
D’Alembert Equation ◽  
Stability And Instability ◽  
Unlimited Growth ◽  
Neumann Type ◽  
Finite Space ◽  
Space Interval

The behavior of energy is studied for the real scalar field satisfying d'Alembert equation in a finite space interval 0<x<a(t); the endpoint a(t) is assumed to move slower than the light and periodically in most parts of the paper. The boundary conditions are of Dirichlet and Neumann type. We give sufficient conditions for the unlimited growth, the boundedness and the periodicity of the energy E. The case of unbounded energy without infinite limit (0< lim inf t→+∞E(t) < lim sup t→+∞E(t)=+∞) is also possible. For the Neumann boundary condition, E may decay to zero as the time tends to infinity. If a is periodic, the solution is determined by a homeomorphism [Formula: see text] of the circle related to a. The behavior of E depends essentially on the number theoretical characteristics of the rotation number of [Formula: see text].

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