human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge groups papers that share a common citing paper.

Details of the hypergraph:
Center hyperedge (induced by source paper "j"):
  Abstract: So applying Corollary 4.3 to the second equation in (47), we conclude that From (38), we then get jg(y n + ~ k( y (51), we obtain jy n + ~ k( From (39) we see that the right-hand side of (54) is bounded by . Since the system _ y = A 1 y k( y )b 2 jyj ev N : (55) Now, suppose lim sup t!1 jy(t)j = &gt; 0. Then jyj ev 2. Since j k(y)j Ljyj, we have and using (56) and (57), we obtain j~yj ev 2(~-1 + -2 )L + -2 ffi : (58) (Note that if the right-hand side of (58) is 1 , then the inequality is trivial since we know from (52) that j~yj ev 1 .) From (53), (56), and (58), we have -2 ffi + N ffi &gt; N . However, from (55) we see that (60) still holds. So we established (60) in all cases. From (40) we then get jyj ev 2 Taking the lim sup t!1 of the left-hand side of (61), we have 1 2 + N("-2 + 1)ffi i.e. 2 N("-2 + 1)ffi. Substituting this into (58) and (61), we get j~yj ev ffi, and jyj ev 2 N("-2 + 1)ffi . So, if we take N = 2 N("-2 + 1)(1 + 2L(~-1 + -2 )) + -2 ; the conclusion follows. To complete the proof, we need to deal with the general case of m &gt; 1 inputs. This is done by induction on m, as in the proof in [14], and will be omitted here. 2 [1] Fuller, A.T., "In the large stability of relay and saturated control systems with linear controllers," Int. J. Control, 10(1969): 457-480. [2] Gutman, P-O., and P. Hagander, "A new design of constrained controllers for linear systems," IEEE Transactions on Automat. Contr. AC-30(1985): 22-23. [3] Kosut, R.L., "Design of linear systems with saturating linear control and bounded states," IEEE Trans. Au-tom. Control AC-28(1983): 121-124. [4] Krikelis, N.J., and S.K. Barkas, "Design of tracking systems subject to actuator saturation and integrator wind-up," Int. J. Control 39(1984): 667-682. [5] Schmitendorf, W.E. and B.R. Barmish, "Null controllability of linear systems with constrained controls," SIAM J. Control and Opt. 18(1980): 327-345. [6] Slemrod, M., "Feedback stabilization of a linear control system in Hilbert space," Math. Control Signals Systems 2(1989): 265-285. [7] Slotine, J-J.E., and W. Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, 1991. [8] Sontag, E.D., "An algebraic approach to bounded controllability of linear systems," Int. J. Control 39(1984): 181-188. [9] Sontag, E.D., "Remarks on stabilization and input-to-state stability," Proc. IEEE CDC, Tampa, Dec. 1989, IEEE Publications, 1989, pp. 1376-1378. [10] Sontag, E.D., Mathematical Control Theory: Deterministic Finite Dimensional Systems, Springer, New York, 1990. [11] Sontag, E.D., and H.J. Sussmann, "Nonlinear output feedback design for linear systems with saturating controls," Proc. IEEE CDC, Honolulu, Dec. 1990, IEEE Publications, 1990, pp. 3414-3416. [12] Sussmann, H. J. and Y. Yang, "On the stabilizability of multiple integrators by means of bounded feedback controls" Proc. IEEE CDC, Brighton, UK, Dec. 1991, IEEE Publications, 1991: 70-73. [13] Teel, A.R., "Global stabilization and restricted tracking for multiple integrators with bounded controls," Systems and Control Letters 18(1992): 165-171. [14] Yang, Y., H.J. Sussmann and E.D. Sontag, "Stabilization of linear systems with bounded controls," Proc. June 1992 NOLCOS, Bordeaux, (M. Fliess, Ed.), IFAC Publications, pp. 15-20. [15] Yang, Y., Global Stabilization of Linear Systems with Bounded Feedback, Ph. D. Thesis, Mathematics Department, Rutgers University, 1993. j~yj ev M (~-1 + -2 ) + ffi-2 ; (50)

Includes members:
  Member "Global Stabilization of Linear Discrete-Time Systems with Bounded Feedback":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "New Characterizations of Input to State Stability")

Question: Please tell me which class the citing paper (i.e., the source paper of the center hyperedge) belongs to. The 7 classes are: Neural_Networks, Reinforcement_Learning, Probabilistic_Methods, Theory, Genetic_Algorithms, Case_Based, Rule_Learning. Directly output the class name.

gpt: Neural_Networks