The Experts below are selected from a list of 21756 Experts worldwide ranked by ideXlab platform
Y.-p. Shih - One of the best experts on this subject based on the ideXlab platform.
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THE COMPUTATION OF WAVELET‐GALERKIN APPROXIMATION ON A Bounded Interval
International Journal for Numerical Methods in Engineering, 1996Co-Authors: M.-q. Chen, C. Hwang, Y.-p. ShihAbstract:This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a Bounded Interval.
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The computation of Wavelet-Galerkin approximation on a Bounded Interval
International Journal for Numerical Methods in Engineering, 1996Co-Authors: M.-q. Chen, C. Hwang, Y.-p. ShihAbstract:This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a Bounded Interval.
Jean-michel Coron - One of the best experts on this subject based on the ideXlab platform.
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on boundary feedback stabilization of non uniform linear 2 2 hyperbolic systems over a Bounded Interval
Systems & Control Letters, 2011Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Conditions for boundary feedback stabilizability of non-uniform linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a basic quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilizing linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilization of open channels represented by linearized Saint–Venant equations with non-uniform steady-states.
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On boundary feedback stabilization of non-uniform linear 2 × 2 hyperbolic systems over a Bounded Interval ✩
Systems & Control Letters, 2011Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Conditions for boundary feedback stabilizability of non-uniform linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a basic quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilizing linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilization of open channels represented by linearized Saint–Venant equations with non-uniform steady-states.
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further results on boundary feedback stabilisation of 2 2 hyperbolic systems over a Bounded Interval
IFAC Proceedings Volumes, 2010Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Abstract Conditions for boundary feedback stabilisability of linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilising linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilisation of open channels represented by Saint-Venant equations with non-uniform steady-states. Copyright © IFAC 2010
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Further Results on Boundary Feedback Stabilisation of 2 × 2 Hyperbolic Systems Over a Bounded Interval
IFAC Proceedings Volumes, 2010Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Abstract Conditions for boundary feedback stabilisability of linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilising linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilisation of open channels represented by Saint-Venant equations with non-uniform steady-states. Copyright © IFAC 2010
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dissipative boundary conditions for one dimensional nonlinear hyperbolic systems
Siam Journal on Control and Optimization, 2008Co-Authors: Jean-michel Coron, Georges Bastin, Brigitte DandreanovelAbstract:We give a new sufficient condition on the boundary conditions for the exponential stability of one-dimensional nonlinear hyperbolic systems on a Bounded Interval. Our proof relies on the construction of an explicit strict Lyapunov function. We compare our sufficient condition with other known sufficient conditions for nonlinear and linear one-dimensional hyperbolic systems.
M.-q. Chen - One of the best experts on this subject based on the ideXlab platform.
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THE COMPUTATION OF WAVELET‐GALERKIN APPROXIMATION ON A Bounded Interval
International Journal for Numerical Methods in Engineering, 1996Co-Authors: M.-q. Chen, C. Hwang, Y.-p. ShihAbstract:This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a Bounded Interval.
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The computation of Wavelet-Galerkin approximation on a Bounded Interval
International Journal for Numerical Methods in Engineering, 1996Co-Authors: M.-q. Chen, C. Hwang, Y.-p. ShihAbstract:This paper describes exact evaluations of various finite integrals whose integrands involve products of Daubechies' compactly supported wavelets and their derivatives and/or integrals. These finite integrals play an essential role in the wavelet-Galerkin approximation of differential or integral equations on a Bounded Interval.
Charles K. Chui - One of the best experts on this subject based on the ideXlab platform.
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On solving first-kind integral equations using wavelets on a Bounded Interval
IEEE Transactions on Antennas and Propagation, 1995Co-Authors: Jaideva C. Goswami, A.k. Chan, Charles K. ChuiAbstract:The conventional method of moments (MoM), when applied directly to integral equations, leads to a dense matrix which often becomes computationally intractable. To overcome the difficulties, wavelet-bases have been used previously which lead to a sparse matrix. The authors refer to "MoM with wavelet bases" as "wavelet MoM". There have been three different ways of applying the wavelet techniques to boundary integral equations: 1) wavelets on the entire real line which requires the boundary conditions to be enforced explicitly, 2) wavelet bases for the Bounded Interval obtained by periodizing the wavelets on the real line, and 3) "wavelet-like" basis functions. Furthermore, only orthonormal (ON) bases have been considered. The present authors propose the use of compactly supported semi-orthogonal (SO) spline wavelets specially constructed for the Bounded Interval in solving first-kind integral equations. They apply this technique to analyze a problem involving 2D EM scattering from metallic cylinders. It is shown that the number of unknowns in the case of wavelet MoM increases by m-1 as compared to conventional MoM, where m is the order of the spline function. Results for linear (m=2) and cubic (m=4) splines are presented along with their comparisons to conventional MoM results. It is observed that the use of cubic spline wavelets almost "diagonalizes" the matrix while maintaining less than 1.5% of relative normed error. The authors also present the explicit closed-form polynomial representation of the scaling functions and wavelets. >
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Wavelets on a Bounded Interval
Numerical Methods in Approximation Theory Vol. 9, 1992Co-Authors: Charles K. Chui, Ewald QuakAbstract:The aim of this paper is to present two different approaches to the study of multiresolution analysis and wavelets on a Bounded Interval. Recently, Meyer obtained orthonormal wavelets on a Bounded Interval by restricting Daubechies’ scaling functions and wavelets to [0, 1] and applying the Gram-Schmidt procedure to orthonormalize the restrictions. Our own approach — presented in the second part of the paper — is based on the semi-orthogonal Chui-Wang spline-wavelets. In this case we no longer have orthogonality in one scale, but there are explicit formulae for these wavelets.
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An analysis of two-dimensional scattering by metallic cylinders using wavelets on a Bounded Interval
Proceedings of IEEE Antennas and Propagation Society International Symposium and URSI National Radio Science Meeting, 1Co-Authors: Jaideva C. Goswami, A.k. Chan, Charles K. ChuiAbstract:Summary form only given. The method of moments (MOM) when applied to integral equations results into a fully-populated matrix which is often ill-conditioned, causing numerical instability and poor convergence in the case of iterative techniques. The condition number increases with the decrease in the step-size of the discretisation. It is now well known that multigrid methods offer a solution to such difficulties. Wavelets, because of their multiresolution properties, are naturally suited for multigrid methods. Their applications to integral equations lead to a well-conditioned matrix. Furthermore, the resultant matrix is sparse because of the local supports and the vanishing moment property of wavelets. The purpose of the paper is to demonstrate the application of semi-orthogonal compactly supported spline-wavelets on a Bounded Interval to resolve integral equations encountered in the two-dimensional electromagnetic scattering by metallic cylinders. In order to achieve a higher degree of sparsity, one must use higher order spline wavelets. However, higher order wavelets have higher spatial supports. The authors restrict themselves to the use of linear and cubic spline wavelets. The results obtained using the wavelet approach and the conventional MOM approach are presented. >
Georges Bastin - One of the best experts on this subject based on the ideXlab platform.
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on boundary feedback stabilization of non uniform linear 2 2 hyperbolic systems over a Bounded Interval
Systems & Control Letters, 2011Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Conditions for boundary feedback stabilizability of non-uniform linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a basic quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilizing linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilization of open channels represented by linearized Saint–Venant equations with non-uniform steady-states.
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On boundary feedback stabilization of non-uniform linear 2 × 2 hyperbolic systems over a Bounded Interval ✩
Systems & Control Letters, 2011Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Conditions for boundary feedback stabilizability of non-uniform linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a basic quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilizing linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilization of open channels represented by linearized Saint–Venant equations with non-uniform steady-states.
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further results on boundary feedback stabilisation of 2 2 hyperbolic systems over a Bounded Interval
IFAC Proceedings Volumes, 2010Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Abstract Conditions for boundary feedback stabilisability of linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilising linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilisation of open channels represented by Saint-Venant equations with non-uniform steady-states. Copyright © IFAC 2010
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Further Results on Boundary Feedback Stabilisation of 2 × 2 Hyperbolic Systems Over a Bounded Interval
IFAC Proceedings Volumes, 2010Co-Authors: Georges Bastin, Jean-michel CoronAbstract:Abstract Conditions for boundary feedback stabilisability of linear 2×2 hyperbolic systems over a Bounded Interval are investigated. The main result is to show that the existence of a quadratic control Lyapunov function requires that the solution of an associated ODE is defined on the considered Interval. This result is used to give explicit conditions for the existence of stabilising linear boundary feedback control laws. The analysis is illustrated with an application to the boundary feedback stabilisation of open channels represented by Saint-Venant equations with non-uniform steady-states. Copyright © IFAC 2010
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dissipative boundary conditions for one dimensional nonlinear hyperbolic systems
Siam Journal on Control and Optimization, 2008Co-Authors: Jean-michel Coron, Georges Bastin, Brigitte DandreanovelAbstract:We give a new sufficient condition on the boundary conditions for the exponential stability of one-dimensional nonlinear hyperbolic systems on a Bounded Interval. Our proof relies on the construction of an explicit strict Lyapunov function. We compare our sufficient condition with other known sufficient conditions for nonlinear and linear one-dimensional hyperbolic systems.
