**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31097

##### Stabilization of Nonnecessarily Inversely Stable First-Order Adaptive Systems under Saturated Input

**Authors:**
M. De la Sen,
O. Barambones

**Abstract:**

**Keywords:**
Control,
Stabilization,
Discrete Systems,
Hybrid dynamic systems,
saturated
input

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1074461

**References:**

[1] M. De la Sen, "Design of a discrete robust linear feedback controller with nonlinear saturating actuator", Int. J. of Systems Sci., Vol. 20 , No. 3, pp. 495-521, 1994.

[2] B. Muller, J. Reinhardt and M.T. Strickland, Physics of Neural Networks. An Introduction, Berlin: Springer Verlag, 1995.

[3] A. Feuer and A.S. Morse, "Adaptive control of single-input singleoutput linear systems", IEEE Trans. Automat. Contr., Vol. AC-23, pp. 557-569, 1978.

[4] A.S. Morse, "Global stability of parameter-adaptive control systems", IEEE Trans. Automat. Contr., Vol. AC-25, No. 3, pp. 433-439, 1980.

[5] K.S. Narendra, Y. Lin and L.S. Valavani," Stable adaptive controller design. Part II: Proof of stability", IEEE Trans. Automat. Contr, Vol. AC-25, No. 3, pp. 440-448, 1980.

[6] R.D. Nussbaum, "A state approach to the problem of adaptive control assignment", MCSS, Vol. 2, pp. 243-246, 1989.

[7] R.D. Nussbaum, "Some remarks on a conjecture in parameter adaptive control ", Systems and Control Letters, Vol. 2, pp. 243-246, 1989.

[8] R. Mudgett and A.S. Morse, "Adaptive stabilization of linear systems with unknown high frequency gains", IEEE Trans. Automat. Contr., Vol. AC-30, pp. 549-554, 1985.

[9] G. Kreisselmeier and M.C. Smith, "Stable adaptive regulation of arbitrary n-th order plants", IEEE Trans. Automat. Contr., Vol. AC-31, pp. 299-305, 1986.

[10] V. Etxebarria and M. De la Sen, "Adaptive control based on special compensation methods for time-varying systems subject to bounded disturbances", Int. J. of Control, Vol. 61, No. 3, pp. 667-694, 1995.

[11] M. De la Sen and A. Pena, " Synthesis of controllers for arbitrary poleplacement in discrete plants including unstable zeros with extensions to adaptive control", J .of the Franklin Institute, Vol. 335.B, No. 3, pp. 471- 502, 1988.

[12] P. De Larminat, "On the stabilization condition in indirect adaptive control", Automatica, Vol. 20, pp. 793-795, 1984.

[13] R. Lozano, A. Osorio and J. Torres, "Adaptive stabilization of nonminimum phase first-order continuous-time systems", IEEE Trans. Automat. Contr., Vol. AC-39, No. 8, pp. 1748-1751, 1992.

[14] R. Lozano and X. Zhao, "Adaptive pole placement without excitation probing signals", IEEE Trans. Automat. Contr., Vol. AC-39, No. 1, pp. 47-58, 1994.

[15] M. De la Sen, "On the robust adaptive stabilization of a class of nominally first-order hybrid systems", IEEE Trans. Automat. Contr., Vol. 44, No. 3, pp. 597-602, 1999.

[16] M. De la Sen, "Robust adaptive stabilization of time- varying first- order hybrid systems with covariance resetting", Int. J. of Nonlinear Mechanics, Vol. 33, No. 1, pp. 1335- 1339, 1997.

[17] T. H. Lee and K. S. Narendra, "Stable discrete adaptive control with unknown high- frequency gain", IEEE Trans. Automat. Contr., Vol. AC- 31, No. 5, pp. 477-479, 1986.

[18] M. De la Sen, "Multirate hybrid adaptive control", IEEE Trans. Automat. Contr., Vol. AC-31, No. 5, pp. 582-586, 1986.

[19] R. Middleton, G.C. Goodwin, D.J. Hill and D.Q. Mayne, "Design issues in adaptive control", IEEE Trans. Automat. Contr., Vol. AC-33 No. 1, pp. 50-58, 1988.

[20] C. A. Desoer and M. Vidyasagar, Feedback Systems: Input - Output Properties, New York: Academic Press, 1975.

[21] N. Luo and M. De la Sen, " State-feedback sliding mode control of a class of uncertain time-delay systems", IEE Proceedings-D Control Theory and Applications, Vol. 140, No. 4, pp. 261-274, 1993.

[22] M. De la Sen and S. Alonso Quesada, "Robust adaptive regulation of potentially inversely unstable first-order systems", Journal of the Franklin Institute- Engineering and Applied Mathematics, Vol. 336, No. 4, pp. 627-648, 1999.

[23] N. Luo, J. Rodellar, J. Vehi and M. De la Sen, "Composite semiactive control of a class of seismically excited structures", Journal of the Franklin Institute- Engineering and Applied Mathematics, Vol. 338, No. 2-3, pp. 225-240, 2001.

[24] N. Luo, J. Rodellar, J. Vehi and M. De la Sen, "Output feedback sliding mode control of base isolated structures", Journal of the Franklin Institute- Engineering and Applied Mathematics, Vol. 337, No. 5, pp. 555-577, 2000.

[25] M. De la Sen, "About the positivity of a class of hybrid dynamic linear systems", Applied Mathematics and Computation, Vol. 189, No. 1, pp. 852-868, 2007.

[26] M. De la Sen, "Quadratic stability and stabilization of switched dynamic systems with uncommensurate internal point delays", Applied Mathematics and Computation, Vol. 185, No. 1, pp. 508-526, 2007.

[27] M. De la Sen, "On positivity of singular regular linear time-delay timeinvariant systems subject to multiple internal and external incommensurate point delays", Applied Mathematics and Computation, Vol. 190, No. 1, pp. 382-401, 2007.