Results 141 to 150 of about 560 (182)
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Riesz Basis Generation: Dual-Basis Approach
2019This chapter is devoted to the Riesz basis property for wave-like equations. It follows the routs from concrete example to abstract framework. This demonstrates the overall technique. In this chapter, the adjoint basis approach in various situations is introduced, which makes use of the Riesz basis property of exponential families, in particular, the ...
Bao-Zhu Guo, Jun-Min Wang
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Riesz basis property of serially connected Timoshenko beams
International Journal of Control, 2007In this paper we study the Riesz basis property of serially connected Timoshenko beams with joint and boundary feedback controls. Suppose that the left end of the whole beam is clamped and the right end is free. At intermediate nodes, the displacement and rotational angle of beams are continuous but the shearing force and bending moment could be ...
Gen-Qi Xu, Zhong-Jie Han, Siu-Pang Yung
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Riesz basis of exponential family for a hyperbolic system
Journal of Applied Analysis, 2019Abstract This paper studies a linear hyperbolic system with boundary conditions that was first studied under some weaker conditions in [8, 11]. Problems on the expansion of a semigroup and a criterion for being a Riesz basis are discussed in the present paper.
Intissar, Abdelkader +2 more
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Riesz Basis Property for Generic Network of Strings
2007 Chinese Control Conference, 2006In this paper, we study the generation problem of Riesz basis for a generic network of strings with joint damping at all vertices. First we give spectral basic property of system operator A. Under certain conditions we prove that the spectrum of A distributes in a strip parallel to the imaginary axis.
Guo Yanni, Xu Genqi, Yang Lingling
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Riesz Basis Generation: Comparison Method
2019This chapter provides a panoramic view on the comparison method. It discusses systematically how the comparison method is used to derive the Riesz basis generation for systems described by partial differential equations. A basic assumption for comparison method to be working is that the feedback can be considered as a perturbation of the system itself,
Bao-Zhu Guo, Jun-Min Wang
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The Riesz Basis Property with Brackets for Dirac Systems with Summable Potentials
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Savchuk, A. M., Sadovnichaya, I. V.
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A Riesz basis approach to exponential stability in thermoelasticity of type III
2013 9th Asian Control Conference (ASCC), 2013Using a Riesz basis approach, we investigate, in this paper, the exponential stability for a one-dimensional linear thermoelasticity of type III with Dirichlet-Dirichlet boundary conditions. A detailed spectral analysis gives that the spectrum of the system contains two parts: the point and continuous spectrum. It is shown that, by asymptotic analysis,
Jing Wang, Jun-Min Wang
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On a Riesz Basis of Finite-Dimensional Invariant Subspaces
2021This chapter is devoted to study the Riesz basis of finite-dimensional invariant subspaces for a class of unbounded perturbations of unbounded normal operators, we study the change of the spectrum and we establish the existence of a Riesz basis of finite-dimensional invariant subspaces under an additional a priori assumption on the spectrum of the ...
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Riesz Basis Property and Stability of Planar Networks of Controlled Strings
Acta Applicandae Mathematicae, 2009The paper studies the basis property of root vectors of star-shaped networks of strings whose exterior ends are clamped and common node has a damping. The main operator determined by the network is non-normal. By the asymptotic technique, it is shown that its spectrum is in a strip parallel to the imaginary axis, and there is a sequence of root vectors
Han, Zhong Jie, Wang, Lei
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Riesz Basis Generation: Green Function Approach
2019In this chapter, we discuss another approach for Riesz basis the so-called Green function approach. This happens for beam equations where the boundary feedback control is of the same order as the original but we cannot apply the approach in Chapter 4 for this situation because the exponential family is usually not Riesz basis for the spectrum not being
Bao-Zhu Guo, Jun-Min Wang
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