Above are papers related to the following paper: [Paper_ID] Paper #1131348. 	[Title] 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) Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #409255. 	[Title] STABILIZATION WITH SATURATED ACTUATORS, A WORKED EXAMPLE:F-8 LONGITUDINAL FLIGHT CONTROL [Abstract] The authors and coworkers recently proved general theorems on the global stabilization of linear systems subject to control saturation. This paper develops in detail an explicit design for the linearized equations of longitudinal flight control for an F-8 aircraft, and tests the obtained controller on the original nonlinear model. This paper represents the first detailed derivation of a controller using the techniques in question, and the results are very encouraging. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1153097. 	[Title]  [Abstract] A General Result on the Stabilization of Linear Systems Using Bounded Controls 1 ABSTRACT We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a "neural-network type" one-hidden layer architecture, while the other one is in terms of cascades of linear maps and saturations. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #7532. 	[Title] On Finite Gain Stabilizability of Linear Systems Subject to Input Saturation [Abstract] This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every L p -norm. Explicit bounds on closed-loop gains are obtained, and they are related to the norms for the respective systems without saturation. These results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple (size &gt; 1) Jordan blocks, contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state-space sense; this is shown in particular for the double integrator. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #7537. 	[Title] Global Stabilization of Linear Discrete-Time Systems with Bounded Feedback [Abstract] This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections ("single hidden layer neural networks") of simple saturation functions. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #141171. 	[Title] New Characterizations of Input to State Stability [Abstract] We present new characterizations of the Input to State Stability property. As a consequence of these results, we show the equivalence between the ISS property and several (apparent) variations proposed in the literature. Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #314459. 	[Title] Input-Output Analysis of Feedback Loops with Saturation Nonlinearities [Abstract]  Please summarise all the given information.

Above are papers related to the following paper: [Paper_ID] Paper #1113534. 	[Title] Avoiding Saturation By Trajectory Reparameterization [Abstract] The problem of trajectory tracking in the presence of input constraints is considered. The desired trajectory is reparameterized on a slower time scale in order to avoid input saturation. Necessary conditions that the reparameterizing function must satisfy are derived. The deviation from the nominal trajectory is minimized by formulating the problem as an optimal control problem. Please summarise all the given information.

Paper #1131348 has the title `j  
` and the 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)
`.
Question: Which category should Paper #1131348 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].


Paper #1131348 has the title `j  
` and the 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)
`.
Question: Which category should Paper #1131348 be classified as ?
You can select one from ['Neural_Networks', 'Case_Based', 'Theory', 'Reinforcement_Learning', 'Probabilistic_Methods', 'Rule_Learning', 'Genetic_Algorithms'].

This paper should be classified into: Neural_Networks