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Article
On proximinality of convex sets in superspaces
In this paper, we show that a closed convex subset C of a Banach space is strongly proximinal (proximinal, resp.) in every Banach space isometrically containing it if and only if C is locally (weakly, resp.) comp...
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Article
Several remarks on ball-coverings of normed spaces
This paper presents two counterexamples about ball-coverings of Banach spaces and shows a new characterization of uniformly non-square Banach spaces via ball-coverings.
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Article
Every weakly compact set can be uniformly embedded into a reflexive Banach space
Based on an application of the Davis-Figiel-Johnson-Pelzyśki procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its applic...
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Book
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Chapter
Introduction
The study of stability originates in mechanics. Early in the 17th century, a principle, called Torricelli’s principle[154]. was already in use: it says that if a system of interconnected heavy bodies is in equili...
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Chapter
Stability of C0-Semigroups
Stability analysis and feedback stabilization are issues of great importance in control system design. In this chapter, we study the stability of the following abstract Cauchy problem on a Danach space X: ...
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Chapter
Dynamic Boundary Control of Vibration Systems Based on Passivity
In this chapter, we consider feedback stabilization of a class of passive infinite dimensional systems by means of dynamic boundary control. The notion of passivity was developed in connection with circuit theory...
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Chapter
Semigroups of Linear Operators
Semigroups of linear operators are closely related to the solution of the following linear differential equation:
(2.1) $$ \do... -
Chapter
Static Sensor Feedback Stabilization of Euler-Bernoulli Beam Equations
In this chapter, we consider stabilization problems of Euler-Bernoulli beam equations arising in the area of space and industrial robots with lightweight and flexible arms, as well as in the area of flexible s...
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Chapter
Other Applications
In Chapter 4, we applied the energy multiplier method and frequency domain criteria to determine the exponential stability of linear dynamic systems which generate C0-semigroups on Danach or Hilbert spaces. For s...
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Article
Stability analysis of a hybrid system arising from feedback control of flexible robots
This paper presents stability analysis for a hybrid system consisting of a coupled partial differential equation and an ordinary differential equation arising from shear force feedback control of flexible robo...
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Chapter and Conference Paper
Dynamics and control of bending and torsional vibrations of flexible beams
