Compensators for singular control systems with delays in outputs

Authors

  • Hernán R. Henríquez Miranda Universidad de Santiago.
  • Genaro Castillo Universidad de Talca.

DOI:

https://doi.org/10.4067/S0716-09172004000300005

Keywords:

Singular control systems, asymptotic observators, asymptotic compensators, asymptotic regulators, sistemas singulares de control, observadores asintónticos, compensadores asintóticos, reguladores asintóticos.

Abstract

In this paper we study the design of dynamic compensators for linear singular control systems described by the equation Ex 0(t) = Ax(t) + Bu(t) with time delayed observed output y(t) = Cx(t - r). The proposed compensators are applied to solve the regulator problem for the mentioned systems with controlled output z(t) = Dx(t).

Author Biographies

Hernán R. Henríquez Miranda, Universidad de Santiago.

Departamento de Matemática.

Genaro Castillo, Universidad de Talca.

Departamento de Matemática.

References

[1] R. Bellman and K. Cooke, “Differential-Difference Equations,” Academic? Press, New York, (1963).?

[2] K. P. M. Bhat and H. N. Koivo, An observer theory for time-delay systems,? IEEE Trans. Aut. Contr. 21, pp. 266-269, (1976).?

[3] S. D. Brierley, J. N. Chiasson, E. B. Lee and S. H. Zak, On stability independent of delay for linear systems, IEEE Trans. Aut. Contr. 27(1), pp. 252-254,? (1982).?

[4] S. L. Campbell, “Singular Systems of Differential Equations,” Pitman Advanced Publishing Program, London, (1980).?

[5] S. L. Campbell, “Singular Systems of Differential Equations II,” Pitman Advanced Publishing Program, London, (1982).?

[6] B-S. Chen, S-S. Wang and H-C. Lu, Stabilization of time-delay systems containing saturating actuators, Int. J. Control 47 (3), pp. 867-881, (1988).?

[7] L. Dai, “ Singular Control Systems,” Lect. Notes in Control and Information? Sciences, 118. Springer Verlag, Berlin, (1989).?

[8] R. Datko, Remarks concerning the asymptotic stability and stabilization of? linear delay differential equations, J. Math. Anal. Appl., 111, pp. 571-584,? (1985).?

[9] G. Doetsh, “ Introduction to the Theory and Application of the Laplace? Transformation,” Springer-Verlag, Berlin, (1974).?

[10] E. Emre, Regulation of linear systems over rings by dynamic output feedback,? Systems and Control Letters 3, pp. 57-62, (1983).?

[11] E. Emre and P. P. Khargonekar, Regulation of split linear systems over rings:? coefficient-assignment and observers, IEEE Trans. Aut. Contr. 27(1), pp. 104-113, (1982).

[12] E. Emre and G. J. Knowles, Control of linear systems with fixed noncommensurate point delays, IEEE Trans. Aut. Contr. 29(12), pp. 1083-1090, (1984).?

[13] M. M. Fahmy and J. O’Reilly, Observers for descriptor systems, Int. J. Control, 49, pp. 2013-2028, (1989).?

[14] F. W. Fairman and A. Kumar, Delayless observers for systems with delay,? IEEE Trans. Aut. Contr. 31(3), pp. 258-259, (1986).?

[15] A. Favini and A. Yagi, “Degenerate Differential Equations in Banach Spaces”,? Marcel Dekker, New York, (1999).?

[16] Y. A. Fiagbedzi and A. E. Pearson, Feedback stabilization of linear autonomous time lag systems, IEEE Trans. Aut. Contr. 31(9), pp. 847-855,? (1986).?

[17] A. Fuchs, V. Lovass-Nagy and R. Mukundan, Output regulator problem of? time-invariant discrete-time descriptor systems, Int. J. Control, 46, pp. 2065-2074, (1987).?

[18] A. Halanay, “Differential Equations,” Academic Press, New York, (1966).?

[19] J. Hale and S. M. Verduyn Lunel, “Introduction to Functional Differential? Equations,” Springer Verlag, New York, (1993).?

[20] M. L. J. Hautus, Controllability and observability conditions of linear autonomous systems, Indag. Math., 31(1969), pp. 443-448, (1969).?

[21] H. Henríquez, Regulator problem for linear distributed control systems with? delays in outputs, Lect. Notes in Pure and Applied Maths. 155, pp. 259-273.? Marcel Dekker, New York, (1994).?

[22] H. R. Henríquez and G. Castillo G., Compensators for singular control systems with small delays in outputs. Revista Proyecciones, 17(1), pp. 23-54,? (1998).?

[23] E. W. Kamen, On the relationship between zero criteria for two-variable? polynomials and asymptotic stability of delay differential equations, IEEE? Trans. Aut. Contr. 25(5), pp. 983-984, (1980).?

[24] E. W. Kamen, Linear systems with commensurate time delays: stability and? stabilization independent of delay, IEEE Trans. Aut. Contr. 27(2), pp. 367-375, (1982).?

[25] E. W. Kamen, Correction to : Linear systems with commensurate time delays:? stability and stabilization independent of delay, IEEE Trans. Aut. Contr.? 28(2), pp. 248-249, (1983).?

[26] E. W. Kamen, P. P. Khargonekar and A. Tannenbaum, Stabilization of? time-delay systems using finite-dimensional compensators, IEEE Trans. Aut.? Contr. 30(1), pp. 75-78, (1985).?

[27] E. W. Kamen, P. P. Khargonekar and A. Tannenbaum, Proper stable Bezout? factorization and feedback control of linear time-delay systems, Int. J. Control? 43(3), pp. 837-857, (1986).?

[28] J. Klamka, Observer for linear feedback control of systems with distributed? delays in controls and outputs, Systems and Control Letters, 1(5), pp. 326-331, (1982).?

[29] F. N. Koumboulis and P. N. Paraskevopoulos, On the pole assignment of? generalized state space systems via state feedback, IEE Proceedings-D, 139,? pp. 106-108, (1992).?

[30] R. M. Lewis and B. Anderson, Necessary and sufficient Conditions for delayindependent stability of linear autonomous systems, IEEE Trans. Aut. Contr.? 25(4)(1980), 735-739, (1980).?

[31] A. Z. Manitius, and A. W. Olbrot, Finite spectrum assignment problem for? systems with delays, IEEE Trans. Aut. Contr. 24(4), pp. 541-553, (1979).?

[32] N. Minamide, N. Arii and Y. Uetake, Design of observers for descriptor systems using a descriptor standard form, Int. J. Control, 50, pp. 2141-2149,? (1989).?

[33] A. W. Olbrot, Stabilizability, detectability and spectrum assignment for linear autonomous systems with general time delays, IEEE Trans. Aut. Contr.,? 23, pp. 887-890, (1978).?

[34] J. O’Reilly, “Observers for Linear Systems,” Academic Press, London, (1983).?

[35] L. Pandolfi, Feedback stabilization of functional differential equations, Boll.? Un. Mat. Ital., 12, pp. 626-635.?

[36] P. N. Paraskevopoulus and F. N. Koumboulis, Decoupling and pole assignment in generalized state space systems, IEE Proceedings-D, 138(6), pp. 547-560, (1991).

[37] P. N. Paraskevopoulos and F. N. Koumboulis, Unifyng approach to observers? for regular and singular systems, IEE Proceedings-D, 138(6), pp. 561-572,? (1991).?

[38] P. N. Paraskevopoulos, F. N. Koumboulis, K. G. Tzierakis and G. E. Panagiotakis, Observer design for generalized state space systems with unknown? inputs, Systems and Control Letters, 18, pp. 309-321, (1992).?

[39] A. Pazy, “Semigroups of Linear Operators and Applications to Partial Differential Equations,” Springer-Verlag, New York, (1983).?

[40] D. Salamon, Observers and duality between observation and state feedback? for time delay systems, IEEE Trans. Aut. Contr. 25(6), pp. 1187-1192, (1980).?

[41] J. M. Schumacher, A direct approach to compensator design for distributed? parameter systems, SIAM J. Contr. Optimiz. 21(6), pp. 823-836, (1983).?

[42] Y. Uetake, Pole assignment and observer design for continuous descriptor? systems, Int. J. Control, 50, pp. 89-96, (1989).?

[43] Q-G. Wang, Y. X. Sun and C. H. Zhou, Finite spectrum assignment for? multivariable delay systems in the frequency domain, Int. J. Control 47(3),? pp. 729-734, (1988).?

[44] K. Watanabe and M. Ito, An observer for linear feedback control laws of multivariable systems with multiple delays in controls and outputs, Systems and? Control Letters, 1(1), pp. 54-59, (1981).?

[45] K. Watanabe, M. Ito and M. Kaneko, Finite spectrum assignment problem for? systems with multiple commensurate delays in state variables, Int. J. Control? 38(5), pp. 913-926, (1983).?

[46] K. Watanabe, M. Ito and M. Kaneko, Finite spectrum assignment problem? for systems with multiple commensurate delays in states and control, Int. J.? Control 39(5), pp. 1073-1082, (1984).?

[47] K. Watanabe and T. Ouchi, An observer of systems with delays in state? variables, Int. J. Control 41(1), pp. 217-229, (1985).?

[48] K. Watanabe, Finite spectrum assignment and observer for multivariable systems with commensurate delays, IEEE Trans. Aut. Contr. 31(6), pp. 543-550,? (1986).?

[49] W. M. Wonham, “Linear Multivariable Control: A Geometric Approach,”? Springer Verlag, Berlin, (1979).?

[50] C-W. Yang and H-L. Tan, Observer design for singular systems with unknown? inputs, Int. J. Control, 49(6), pp. 1937-1946, (1989).?

Published

2017-05-22

How to Cite

[1]
H. R. Henríquez Miranda and G. Castillo, “Compensators for singular control systems with delays in outputs”, Proyecciones (Antofagasta, On line), vol. 23, no. 3, pp. 253-279, May 2017.

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Section

Artículos