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Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator

Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator,10.1016/S0167-6911(01)00201-8,Systems & Control Lett

Controllability and stability of a second-order hyperbolic system with collocated sensor/actuator   (Citations: 30)
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A second-order hyperbolic system with collocated sensor/actuator is considered. The semigroup generation is shown for the closed-loop system under the feedback of a generic unbounded observation operator. The equivalence between the exponential stability of the closed-loop system and exact controllability of the open-loop system is established in the general framework of well-posed 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. 45-65, 2002
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    • ...The system considered in [17] exemplifies the abstract secondorder infinite-dimensional systems ([13])...

    Bao-Zhu Guoet al. Output Feedback Stabilization of a One-Dimensional 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 Chaiet al. Well-posedness and regularity of weakly coupled wave-plate 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...

    Bao-Zhu Guoet 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 well-posedness 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 Weisset al. Exponential Stabilization of a Rayleigh Beam Using Collocated Control

    • ...2 ) × H, system (1) can be formulated as a SISO second-order collocated system [9, 10]:...
    • ...orem 5.8]. By this fact, a second-order collocated system, falling into the framework discussed in [9], must be regular as well if it is well-posed...
    • ...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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