Series in Contemporary Mathematics
Volume 1 / 2015 to Volume 5 / 2024
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Book Series
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Chapter
Introduction
In the monograph [40], we have made an abundant study on the boundary synchronization for a coupled system of wave equations.
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Chapter
Approximate Internal Controllability
In this chapter we show that the classic Kalman’s rank condition is not only necessary but also sufficient for the uniqueness of solution to the adjoint system
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Chapter
Approximate Internal Synchronization
The exact boundary synchronization has been studied for the coupled systems governed by PDEs since the year 2012 in [32, 33].
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Chapter
Stability of Exact Internal Synchronization
In this chapter, we will establish the equivalence between the non approximate controllability and the independence of exactly synchronizable state with respect to applied controls. The main idea consists of u...
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Chapter
Exact Internal Synchronization by Groups
In order to consider the situation that the number of internal controls is further reduced, in this chapter we investigate the exact internal synchronization by groups for system (I).
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Chapter
Algebraic Preliminaries
For the sake of reading, here we collect some useful algebraic results, some of them can be found in the monograph [40].
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Chapter
Approximate Internal Synchronization by Groups
In this chapter, we will clarify that the independence of approximately synchronizable state by groups with respect to applied controls the non extensibility to other approximate synchronization, the linear in...
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Chapter
Exact Internal Synchronization
In this chapter, based on the results given by Chap. 7, the exact internal synchronization and related topics will be discussed.
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Chapter
Stability of Exact Internal Synchronization by Groups
In this chapter, we will deepen the consideration in the previous chapter and show that the state variable can be divided into three groups: the first ...
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Book
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Chapter
Approximate Mixed Controllability
We will show that Kalman’s rank condition is still necessary and sufficient for the uniqueness of solution to the adjoint system associated with incomplete internal and boundary observations, therefore for the...
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Chapter
Exact Mixed Controllability
Under a suitable balanced distribution of observations, system \((I\!\!I^*)\) ( ...
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Chapter
Exact Internal Controllability
In this chapter, we show that system (I) possesses the exact controllability if and only if \({{\,\textrm{rank}\,}}(D)= N\) ...
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Chapter
Family of Exact Internal Synchronizations
The goal of this chapter is to extend the previous study from a specific grou** to the general grou**s. As a result we will examine the possibility to realize several exact internal synchronizations by gro...
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Chapter
Approximate Mixed Synchronization by Groups
In this chapter, we will study the approximate internal synchronization by groups under the internal and boundary controls such as the necessity of the condition of
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Chapter
Exact Mixed Synchronization by Groups
In this chapter we consider the exact synchronization by groups under mixed controls, and study the necessity of the condition of \(C_p\) ...
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Chapter
Indirect Internal Controls
The notion of the indirect dam** was introduced by Russell [1] in the early 1967s.
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Article
Exact Internal Controllability and Synchronization for a Coupled System of Wave Equations
In this paper the exact internal controllability for a coupled system of wave equations with arbitrarily given coupling matrix is established. Based on this result, the exact internal synchronization and the e...
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Article
Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems II: Case of Multiple Feedback Dam**s
In this paper, the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dam**s. They first show that under the observability of a scalar equation, Kalman’s ra...
