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Keywords
(5)
Exact Controllability
Exponential Stability
Hyperbolic System
wellposed linear system
Second Order
Related Publications
(5)
Regular linear systems governed by a boundary controlled heat equation
Parabolic singular limit of a wave equation with localized boundary damping
Stabilization of second order evolution equations by a class of unbounded feedbacks
Riesz basis property of a secondorder hyperbolic system with collocated scalar inputoutput
Admissible input elements for systems in Hilbert space and a Carleson measure criterion
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Controllability and stability of a secondorder hyperbolic system with collocated sensor/actuator
Controllability and stability of a secondorder hyperbolic system with collocated sensor/actuator,10.1016/S01676911(01)002018,Systems & Control Lett
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Controllability and stability of a secondorder hyperbolic system with collocated sensor/actuator
(
Citations: 30
)
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BaoZhu Guo
,
YueHu Luo
A secondorder
hyperbolic system
with collocated sensor/actuator is considered. The semigroup generation is shown for the closedloop system under the feedback of a generic unbounded observation operator. The equivalence between the
exponential stability
of the closedloop system and
exact controllability
of the openloop system is established in the general framework of wellposed linear systems. Finally, the conditions are weakened for the diagonal semigroups with finite dimensional inputs. Example of beam equation is presented to display the application.
Journal:
Systems & Control Letters  SYST CONTROL LETT
, vol. 46, no. 1, pp. 4565, 2002
DOI:
10.1016/S01676911(01)002018
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Citation Context
(18)
...The system considered in [17] exemplifies the abstract secondorder infinitedimensional systems ([
13
])...
BaoZhu Guo
,
et al.
Output Feedback Stabilization of a OneDimensional Schrödinger Equatio...
...In Sec. 2, we cast system (1.1) into an abstract setting studied in [5,
6
]...
...system (2.6) has been studied in detail in [5] and [
6
], respectively...
Shugen Chai
,
et al.
Wellposedness and regularity of weakly coupled waveplate equation wi...
...It then follows from [
13
] that there exists a unique solution to (42) such that (w(¢ , t), wt(¢ , t)) ∈ C(τ, ∞; H). In the sequel we may assume without loss of generality that the solution of (42) is a classical solution...
BaoZhu Guo
,
et al.
Output Stabilization of Euler Beam with Time Delay
...Here, we mention only some of the papers that refer to beams andplatesandwhichobtainexponentialstabilitybystaticoutput feedback through collocated control and observation: Chen [3], [4], Rebarber [11], Triggiani [16], Tucsnak and Weiss [17], Luo et al. [10], Guo and Luo [
8
], and Ammari and Tucsnak [2]...
...Such systems, but with C 1 =0 (hence E =0 ), have been considered in [2], [
8
], and [24]...
...To check the wellposedness of the system Σ, according to the criterion in Curtain and Weiss [5], it remains to show that its transferfunction Gfrom(4.10)isproper.Thiswouldbedifficult to show using eigenfunction expansions, as the discussion (in particular, the counterexamples) in [
8
] show...
George Weiss
,
et al.
Exponential Stabilization of a Rayleigh Beam Using Collocated Control
...2 ) × H, system (1) can be formulated as a SISO secondorder collocated system [
9
, 10]:...
...orem 5.8]. By this fact, a secondorder collocated system, falling into the framework discussed in [
9
], must be regular as well if it is wellposed...
...Same to [
9
], the transfer function is easily computed to be...
...By (17), it is known that [
9
] ˜ b is an admissible input operator, and so is ˜ b ∗ as an output operator...
Jinde Chang
.
Identification of variable coefficients for vibrating systems by bound...
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Citations
(30)
Stabilization of onedimensional Schrödinger equation with variable coefficient under delayed boundary output feedback
KunYi Yang
,
CuiZhen Yao
Published in 2011.
Exponential stability of infinite dimensional linear stochastic systems with time delay
Xisheng Dai
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Feiqi Deng
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Wenguang Luo
Published in 2011.
QCW diodepumped 654 W AO Qswitched Nd:YAG rod oscillatoramplifier laser
Xiaodong Yang
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Qingjun Peng
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Aicong Geng
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Optik
, vol. 122, no. 6, pp. 467470, 2011
Output Feedback Stabilization of a OneDimensional Schrödinger Equation by Boundary Observation With Time Delay
(
Citations: 1
)
BaoZhu Guo
,
KunYi Yang
Journal:
IEEE Transactions on Automatic Control  IEEE TRANS AUTOMAT CONTR
, vol. 55, no. 5, pp. 12261232, 2010
Dynamic stabilization of an EulerBernoulli beam equation with time delay in boundary observation
(
Citations: 8
)
Baozhu Guo
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Kunyi Yang
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