跳变时滞系统的鲁棒控制与滤波器设计
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摘要
时滞不确定性和执行器饱和在实际控制系统中是普遍存在的。它们的存在使得系统的分析与综合变得复杂和困难,同时也往往是导致系统不稳定和系统性能变差的根源。此外,马尔科夫(Markov)跳变系统是一类特殊的随机系统,它能够描述很多的工程系统,更为真实地反映了系统参数变动。因此,跳变时滞系统的研究具有十分重要的理论意义和实际应用价值。
基于Lyapunov稳定性理论,以线性矩阵不等式(LMI)为主要工具,本文讨论跳变时滞系统的鲁棒控制与滤波器设计问题。全文主要研究内容如下:
1、针对含有饱和执行器约束的跳变时滞不确定系统研究了鲁棒保性能控制问题。目标是设计控制器,使得对容许的不确定性,闭环系统是鲁棒稳定的,并且满足所提的保性能指标。
2、针对含有Markov跳变参数的不确定时滞系统研究了鲁棒保性能滤波问题。目标是设计滤波器,使得对容许的不确定性,滤波误差系统鲁棒稳定的,并且满足所提的保性能指标。
文中大部分结果是基于LMI方法的,这种方法的关键在于把控制目标用线性矩阵不等式表示,把控制器参数用线性矩阵不等式的解表示。
Time-delay systems and systems with actuator saturation exist quite widely in real control systems. The existence of them makes the system analysis and synthesis become more complicated and difficult. Meanwhile, the existence of them is frequently a source of instability and performance degradation in many dynamic systems. In addition, the Markovian jumping system is a kind of special stochastic system. It can describe many project systems and reflect the existing of the variation of the system parameter. Thus, it is of a great importance in theoretical and practical application to study the robust control for the time-delay systems with Markovin jumping parameters.
Based on Lyapunov stability theory, this dissertation devotes on the robust control and filter for time-delay systems with Markovin jumping parameters by LMI. The main work of this dissertation is outlined as follows:
1、Robust guaranteed cost control for time-delay systems with actuator saturation and Markovian jumping parameters is proposed. The objective is to design controllers such that for all uncertainties, the resulting closed system is robust stable and satisfies the proposed guaranteed cost performance.
2、Robust guaranteed cost filter for time-delay systems with Markovian jumping parameters is proposed. The objective is to design filters such that for all uncertainties, the filtering error system is robust stable and satisfies the proposed guaranteed cost performance.
The most results of this dissertation are presented by means of LMIs. The key to this method is to express the control objectives by means of LMIs, and to express the parameters of controllers in terms of the solutions to LMI.
基于Lyapunov稳定性理论,以线性矩阵不等式(LMI)为主要工具,本文讨论跳变时滞系统的鲁棒控制与滤波器设计问题。全文主要研究内容如下:
1、针对含有饱和执行器约束的跳变时滞不确定系统研究了鲁棒保性能控制问题。目标是设计控制器,使得对容许的不确定性,闭环系统是鲁棒稳定的,并且满足所提的保性能指标。
2、针对含有Markov跳变参数的不确定时滞系统研究了鲁棒保性能滤波问题。目标是设计滤波器,使得对容许的不确定性,滤波误差系统鲁棒稳定的,并且满足所提的保性能指标。
文中大部分结果是基于LMI方法的,这种方法的关键在于把控制目标用线性矩阵不等式表示,把控制器参数用线性矩阵不等式的解表示。
Time-delay systems and systems with actuator saturation exist quite widely in real control systems. The existence of them makes the system analysis and synthesis become more complicated and difficult. Meanwhile, the existence of them is frequently a source of instability and performance degradation in many dynamic systems. In addition, the Markovian jumping system is a kind of special stochastic system. It can describe many project systems and reflect the existing of the variation of the system parameter. Thus, it is of a great importance in theoretical and practical application to study the robust control for the time-delay systems with Markovin jumping parameters.
Based on Lyapunov stability theory, this dissertation devotes on the robust control and filter for time-delay systems with Markovin jumping parameters by LMI. The main work of this dissertation is outlined as follows:
1、Robust guaranteed cost control for time-delay systems with actuator saturation and Markovian jumping parameters is proposed. The objective is to design controllers such that for all uncertainties, the resulting closed system is robust stable and satisfies the proposed guaranteed cost performance.
2、Robust guaranteed cost filter for time-delay systems with Markovian jumping parameters is proposed. The objective is to design filters such that for all uncertainties, the filtering error system is robust stable and satisfies the proposed guaranteed cost performance.
The most results of this dissertation are presented by means of LMIs. The key to this method is to express the control objectives by means of LMIs, and to express the parameters of controllers in terms of the solutions to LMI.
引文
1. E. J. Davision. The output control of linear time invariant multivariable systems with unmeasurable arbitrary disturbance. IEEE Transaction on Automatic Control, 1971, 17: 621-630
2. J. B. Pearson, P. W. Staats. Robust controllers for linear regulators. IEEE Transaction on Automatic Control, 1974, 19: 231-234
3. G. Zames. Functional analysis applied to nonlinear feedback systems. IEEE Transaction on Circuit Theory, 1963, 10: 392-404
4. R. E. Kalman. When is a linear control system optimal?. Transaction ASME, Ser. D, 1964, 86: 51-60
5. J. C. Doyle. Analysis of control systems with structured uncertainty. IEE Proc. Part D, 129: 242-250
6. J. C. Doyle, B. A. Francis, and Tennenbaum. Feedback control theory. Macmillan Publishing Company, New York
7. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solution to standard H 2 and H∞control problem. IEEE Transaction on Automatic Control, 1989, 34(8): 831-847
8.解学书,钟宜生. H∞控制理论.北京:清华大学出版社,1994
9.梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用,北京:清华大学出版社,2003
10. K. Zhou and P. P. Khargonekar. An algebraic Riccati equation approach to H∞optimization. 1988, Syst. Contr. Lett., 11: 85-91
11. T. Iwasaki and R. R. Skelton. All controllers for the general H∞control problem: LMI existence conditions and state space formulas. Automatica, 1994, 30(8): 1307-1317
12. V. L. Kharitonov. Asymptotic stability of an equlibrium position of a family of systems of linear differential equations. Differentsialjnie Uravnenija, 1978, 14: 2086-2088
13. A. C. Barmish, C. V. Hollot, and Huang Lin. Root locations of an entire polytope of polynomials: it suffices to check the edges, Math. Control, Signal, and Systems, 1988, 1: 61-71
14. H. Chapellat, and S. P. Bhattacharyya. A generalization of Kharitonv’s theorem:robust stability of interval plants. IEEE Transaction on Automatic Control, 1989, 34(3): 306-311
15. W. Chen and I. R. Petersen. A class of multilinear uncertain polynomials to which the edge theorem is applicable. IEEE Transaction on Automatic Control, 1995, 40(12): 2103-2107
16. R. V. Monopoli. Engineering aspects of control system design via the direct method of Lyapunov. NASA Report, 1966, CR-654
17. G. Leitmann. Guaranteed asymptotic stability for some linear systems with bounded uncertainties. ASME J. Dynamical Systems, Measurement and Control, 1979, 101(2): 212-216
18. B. R. Barmish and G. Leitmann. On ultimate bounded control of uncertain system in the absence of matching conditions. IEEE Transaction on Automatic Control, 1982, 27(1): 153-157
19. Y. H. Chen and G. Leitmann. Robustness of uncertain systems in the absence of matching assumptions. Int. J. Control, 1987, 45(5): 1527-1542
20. I. R. Petersen and C. V. Hollet. A Riccati equation approach to the stabilization of uncertain linear systems. Automatica, 1986, 22: 397-411
21. I. R. Petersen. Disturbance attenuation and H∞optimization: a design method based on the algebraic Riccati equation. IEEE Transaction on Automatic Control, 1987, 32: 427-429
22. M. A. Rotea and P. P. Khargonekar. Stabilization of uncertain systems with norm bounded uncertainty- A control Lyapunov function approach. SIAM J. Control Optim., 1989, 27(6): 1462-1467
23. L. Yu, J. Chu, and H. Su. Robust memoryless H∞controller design for linear time-delay systems with norm-bounded time-varying uncertainty, Automatica, 1996, 32(12): 1759-1762
24. R. E. Kalman. A new approach to linear filtering and prediction. Transactions of ASME, Journal of Basic Engineering. 1960, 82: 34-45
25. D. G. Luenberger. An introduction to observers. IEEE Transaction on Automatic Control, 1971, 16(6): 596-602
26. R. M. Palhares, P. L. D. Peters. Robust H∞filter design with pole constraints for discrete-time systems. Journal of Franklin Institute, 2000, 237: 1696-1703
27. H. J. Gao, C. H. Wang. Robust L2 ? L∞filtering for uncertain systems with multiple time-varying delays. IEEE Trans. on Circuits and Systems, vol. 50, pp.594-599, 2003
28. R. M. Palhares, P. L. D. Peres. Robust filtering with guaranteed energy-to-peak performance-an LMI approach. Automatica, 2000, 36: 851-858
29.高会军,王常虹.不确定离散系统的鲁棒l 2? l∞滤波与H∞滤波新方法.中国科学,2003, 33(8): 696-704
30. K. Nagpal, J. Abedor, K. Pilooa. A linear matrix inequality approach to peak-peak gain minimization. Int. J. Robust Nonlinear Contr., 1996, 6: 899-927
31. T. Vincent, J. Abedor, K. Nagpal, et al. Discrete-time estimators with guaranteed peak-peak performance. Proceeding of the 13th IFAC Triennial World Congress, San Francisco, 1996, 43-48
32. J. Kim, D. Oh, H. Park, Guaranteed cost and H∞filtering for time-delay systems. Proceeding of the American Control Conference, 2001: 4014-4018
33. D. Sworder. Feedback control of a class of linear systems with jumping parameters. IEEE Trans. on Automatic Control, 1969, 14:9-14
34. M. Martin. On controllability of linear systems with stochastic jump parameters. IEEE Trans. on Automatic Control, 1986, 31:680-683
35. D. O. D. Farias, J. C. Geromel, B. R. Do, and O. L. Costa. Output feedback control of Markov jump linear systems. IEEE Trans. on Automatic Control, 2000, 45(5): 944-949
36. X. B. Feng, K. A. Loparo, Y. D. Ji, and H. J. Chizeck. Stochastic stability properties of jump linear systems. IEEE Trans. on Automatic Control 1992, 37: 38-53
37.付艳明.跳变时滞不确定系统的鲁棒控制与滤波.哈尔滨工业大学博士论文. 2006年4月
38. E. K. Boukas and P. Shi. Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters. Int. J. Robust nonlinear Control, 1998, 8: 1155-1167
39. X. R. Mao. Exponential stability of stochastic delay internal systems with Markovian switching. IEEE Trans. on Automatic Control, 2002, 47(10): 1604-1612
40. Y. Y. Cao and J. Lam. Robust H∞control of uncertain Markovian jump systems with time-delay. IEEE Trans. on Automatic Control, 2000, 45(1): 77-85
41. A. T. Fuller. In the large stability of relay and saturating control systems withlinear controllers. International Journal of Control, 1969, 10(4): 457-480
42. J. L. Lemay. Recoverable and reachable zones for linear systems with linear plants and bounded controller outputs IEEE trans. Automat. Control, 1964, 9(2): 346-354
43. W. E. Schmitendorf, B. R. Barmish. Null controllability of linear systems with constrained controls. SIAM Journal of Control and optimization, 1980, 18(4): 327-345
44. E. D. Sontag, H. J. Sussmann. Nonlinear output feedback design for linear systems with saturating control. Proceedings of the conference on Decision and Control, 1990: 3414-3416.
45. F. Tyan, D. S. Bernstein. Global stabilization for systems containing a double integrator using a saturated linear controller. International Journal of Robust and Nonlinear Control, 1999, 9(15): 1143-1156.
46. J. Goncalves. Quadratic surface Lyapunov functions in global stability analysis of saturating systems. Proceedings of the American Control Conference, 1990: 4183-4185.
47. E. T. Jeung, D. C. Oh, J. H. Kim and H. B. Park. Robust controller design for uncertain system with time delays: LMI approach. Automatic, 1996 32(8): 1229-1231
48. X. Li and G. E. de souze. Delay-dependent robust stability and stabilization of uncertain linear delay system: A linear matrix inequality approach. IEEE Trans. on Automat. Contr., 1997, 42(8): 1144-1148
49. E. K. Boukas and Z. K. Liu. Delay-dependent robust stability and stabilization of uncertain linear system with discrete and distributed time-delays. In Proceedings of the American Control Conference, 2001, 3370-3375
50. S. I. Niculescu, C. E. Souza, L. Duard and J. M. Dion. Robust exponential stability of uncertain systems with time-varying delays. IEEE Trans. on Automat.Contr., 1998, 43(5): 743-748
51.俞立,潘海天.具有时变不确定线性系统的鲁棒无源控制.自动化学报,1998,24(3): 368-372
52.李志虎,邵惠鹤.时滞系统输出反馈无源控制器设计.应用科学学报,2001,19(4): 303-307
53.董心壮,张庆灵,郭凯.滞后广义系统的无源控制.黑龙江大学学报,2003,20:72-75
54. J. J. Yan, J. S. Tsai and F. C. kung. A new result on the robust stability of uncertainty systems with time-varying delay. IEEE Trans. On Circuits and Systems, 2001, 48(7): 914-916
55. T. J. Su, C. Y. Lu and J. G. Jong. A LMI approach for robust stability of linear uncertainty systems with time-varying multiple state delays. In Proceedings of the 39th IEEE Conference on Decision and Control, 2000, 1507-1508
56. H. S. Wu and K. Mizukami. Robust stability criteria for dynamic system include delayed perturbations. IEEE Trans. on Automat. Contr., 1995, 40(3): 487-490
57. G. R. Duan and X. X. Liu. A sufficient condition for stability of time- delay system. Control and decision, 1996, 11: 420-423
58. J. Hale and S.M. Verduyn Lunel. Introduction to functional differential equations. SpringerVerlag, New York, 1993
59. D. Y. Khusainov and E.V. Yunkova. Investigation of the stability of linear systems of neutral type by the Lyapunov function method. Differentsialnye Uravneniya, 1988, 24: 613-621
60. J. X. Kuang, J. X. Xiang and H. J. Tian. The asymptotic stability of one-parameter methods for neutral differential equations. BIT, 1994, 34: 400-408
61. J. H. Park and S. Won. A note on stability of neutral delay-differential systems. Journal of the Franklin Institute, 1999, 336: 543-548
62. J. H. Park and S. Won. Asymptotic stability of neutral systems with multiple delays. Journal of Optimization Theory and Applications, 1999, 103: 187-200
63. E. N. Chukwu. Stability and time-optimal control of hereditary Systems, Academic Press, New York, 1992
64. T. J. Tarn, T. Yang, X. Zeng and C.Guo. Periodic output feedback stabilization of neutral systems. IEEE Transactions on Automatic Control, 1996, 41: 511-521
2. J. B. Pearson, P. W. Staats. Robust controllers for linear regulators. IEEE Transaction on Automatic Control, 1974, 19: 231-234
3. G. Zames. Functional analysis applied to nonlinear feedback systems. IEEE Transaction on Circuit Theory, 1963, 10: 392-404
4. R. E. Kalman. When is a linear control system optimal?. Transaction ASME, Ser. D, 1964, 86: 51-60
5. J. C. Doyle. Analysis of control systems with structured uncertainty. IEE Proc. Part D, 129: 242-250
6. J. C. Doyle, B. A. Francis, and Tennenbaum. Feedback control theory. Macmillan Publishing Company, New York
7. J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis. State-space solution to standard H 2 and H∞control problem. IEEE Transaction on Automatic Control, 1989, 34(8): 831-847
8.解学书,钟宜生. H∞控制理论.北京:清华大学出版社,1994
9.梅生伟,申铁龙,刘康志.现代鲁棒控制理论与应用,北京:清华大学出版社,2003
10. K. Zhou and P. P. Khargonekar. An algebraic Riccati equation approach to H∞optimization. 1988, Syst. Contr. Lett., 11: 85-91
11. T. Iwasaki and R. R. Skelton. All controllers for the general H∞control problem: LMI existence conditions and state space formulas. Automatica, 1994, 30(8): 1307-1317
12. V. L. Kharitonov. Asymptotic stability of an equlibrium position of a family of systems of linear differential equations. Differentsialjnie Uravnenija, 1978, 14: 2086-2088
13. A. C. Barmish, C. V. Hollot, and Huang Lin. Root locations of an entire polytope of polynomials: it suffices to check the edges, Math. Control, Signal, and Systems, 1988, 1: 61-71
14. H. Chapellat, and S. P. Bhattacharyya. A generalization of Kharitonv’s theorem:robust stability of interval plants. IEEE Transaction on Automatic Control, 1989, 34(3): 306-311
15. W. Chen and I. R. Petersen. A class of multilinear uncertain polynomials to which the edge theorem is applicable. IEEE Transaction on Automatic Control, 1995, 40(12): 2103-2107
16. R. V. Monopoli. Engineering aspects of control system design via the direct method of Lyapunov. NASA Report, 1966, CR-654
17. G. Leitmann. Guaranteed asymptotic stability for some linear systems with bounded uncertainties. ASME J. Dynamical Systems, Measurement and Control, 1979, 101(2): 212-216
18. B. R. Barmish and G. Leitmann. On ultimate bounded control of uncertain system in the absence of matching conditions. IEEE Transaction on Automatic Control, 1982, 27(1): 153-157
19. Y. H. Chen and G. Leitmann. Robustness of uncertain systems in the absence of matching assumptions. Int. J. Control, 1987, 45(5): 1527-1542
20. I. R. Petersen and C. V. Hollet. A Riccati equation approach to the stabilization of uncertain linear systems. Automatica, 1986, 22: 397-411
21. I. R. Petersen. Disturbance attenuation and H∞optimization: a design method based on the algebraic Riccati equation. IEEE Transaction on Automatic Control, 1987, 32: 427-429
22. M. A. Rotea and P. P. Khargonekar. Stabilization of uncertain systems with norm bounded uncertainty- A control Lyapunov function approach. SIAM J. Control Optim., 1989, 27(6): 1462-1467
23. L. Yu, J. Chu, and H. Su. Robust memoryless H∞controller design for linear time-delay systems with norm-bounded time-varying uncertainty, Automatica, 1996, 32(12): 1759-1762
24. R. E. Kalman. A new approach to linear filtering and prediction. Transactions of ASME, Journal of Basic Engineering. 1960, 82: 34-45
25. D. G. Luenberger. An introduction to observers. IEEE Transaction on Automatic Control, 1971, 16(6): 596-602
26. R. M. Palhares, P. L. D. Peters. Robust H∞filter design with pole constraints for discrete-time systems. Journal of Franklin Institute, 2000, 237: 1696-1703
27. H. J. Gao, C. H. Wang. Robust L2 ? L∞filtering for uncertain systems with multiple time-varying delays. IEEE Trans. on Circuits and Systems, vol. 50, pp.594-599, 2003
28. R. M. Palhares, P. L. D. Peres. Robust filtering with guaranteed energy-to-peak performance-an LMI approach. Automatica, 2000, 36: 851-858
29.高会军,王常虹.不确定离散系统的鲁棒l 2? l∞滤波与H∞滤波新方法.中国科学,2003, 33(8): 696-704
30. K. Nagpal, J. Abedor, K. Pilooa. A linear matrix inequality approach to peak-peak gain minimization. Int. J. Robust Nonlinear Contr., 1996, 6: 899-927
31. T. Vincent, J. Abedor, K. Nagpal, et al. Discrete-time estimators with guaranteed peak-peak performance. Proceeding of the 13th IFAC Triennial World Congress, San Francisco, 1996, 43-48
32. J. Kim, D. Oh, H. Park, Guaranteed cost and H∞filtering for time-delay systems. Proceeding of the American Control Conference, 2001: 4014-4018
33. D. Sworder. Feedback control of a class of linear systems with jumping parameters. IEEE Trans. on Automatic Control, 1969, 14:9-14
34. M. Martin. On controllability of linear systems with stochastic jump parameters. IEEE Trans. on Automatic Control, 1986, 31:680-683
35. D. O. D. Farias, J. C. Geromel, B. R. Do, and O. L. Costa. Output feedback control of Markov jump linear systems. IEEE Trans. on Automatic Control, 2000, 45(5): 944-949
36. X. B. Feng, K. A. Loparo, Y. D. Ji, and H. J. Chizeck. Stochastic stability properties of jump linear systems. IEEE Trans. on Automatic Control 1992, 37: 38-53
37.付艳明.跳变时滞不确定系统的鲁棒控制与滤波.哈尔滨工业大学博士论文. 2006年4月
38. E. K. Boukas and P. Shi. Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters. Int. J. Robust nonlinear Control, 1998, 8: 1155-1167
39. X. R. Mao. Exponential stability of stochastic delay internal systems with Markovian switching. IEEE Trans. on Automatic Control, 2002, 47(10): 1604-1612
40. Y. Y. Cao and J. Lam. Robust H∞control of uncertain Markovian jump systems with time-delay. IEEE Trans. on Automatic Control, 2000, 45(1): 77-85
41. A. T. Fuller. In the large stability of relay and saturating control systems withlinear controllers. International Journal of Control, 1969, 10(4): 457-480
42. J. L. Lemay. Recoverable and reachable zones for linear systems with linear plants and bounded controller outputs IEEE trans. Automat. Control, 1964, 9(2): 346-354
43. W. E. Schmitendorf, B. R. Barmish. Null controllability of linear systems with constrained controls. SIAM Journal of Control and optimization, 1980, 18(4): 327-345
44. E. D. Sontag, H. J. Sussmann. Nonlinear output feedback design for linear systems with saturating control. Proceedings of the conference on Decision and Control, 1990: 3414-3416.
45. F. Tyan, D. S. Bernstein. Global stabilization for systems containing a double integrator using a saturated linear controller. International Journal of Robust and Nonlinear Control, 1999, 9(15): 1143-1156.
46. J. Goncalves. Quadratic surface Lyapunov functions in global stability analysis of saturating systems. Proceedings of the American Control Conference, 1990: 4183-4185.
47. E. T. Jeung, D. C. Oh, J. H. Kim and H. B. Park. Robust controller design for uncertain system with time delays: LMI approach. Automatic, 1996 32(8): 1229-1231
48. X. Li and G. E. de souze. Delay-dependent robust stability and stabilization of uncertain linear delay system: A linear matrix inequality approach. IEEE Trans. on Automat. Contr., 1997, 42(8): 1144-1148
49. E. K. Boukas and Z. K. Liu. Delay-dependent robust stability and stabilization of uncertain linear system with discrete and distributed time-delays. In Proceedings of the American Control Conference, 2001, 3370-3375
50. S. I. Niculescu, C. E. Souza, L. Duard and J. M. Dion. Robust exponential stability of uncertain systems with time-varying delays. IEEE Trans. on Automat.Contr., 1998, 43(5): 743-748
51.俞立,潘海天.具有时变不确定线性系统的鲁棒无源控制.自动化学报,1998,24(3): 368-372
52.李志虎,邵惠鹤.时滞系统输出反馈无源控制器设计.应用科学学报,2001,19(4): 303-307
53.董心壮,张庆灵,郭凯.滞后广义系统的无源控制.黑龙江大学学报,2003,20:72-75
54. J. J. Yan, J. S. Tsai and F. C. kung. A new result on the robust stability of uncertainty systems with time-varying delay. IEEE Trans. On Circuits and Systems, 2001, 48(7): 914-916
55. T. J. Su, C. Y. Lu and J. G. Jong. A LMI approach for robust stability of linear uncertainty systems with time-varying multiple state delays. In Proceedings of the 39th IEEE Conference on Decision and Control, 2000, 1507-1508
56. H. S. Wu and K. Mizukami. Robust stability criteria for dynamic system include delayed perturbations. IEEE Trans. on Automat. Contr., 1995, 40(3): 487-490
57. G. R. Duan and X. X. Liu. A sufficient condition for stability of time- delay system. Control and decision, 1996, 11: 420-423
58. J. Hale and S.M. Verduyn Lunel. Introduction to functional differential equations. SpringerVerlag, New York, 1993
59. D. Y. Khusainov and E.V. Yunkova. Investigation of the stability of linear systems of neutral type by the Lyapunov function method. Differentsialnye Uravneniya, 1988, 24: 613-621
60. J. X. Kuang, J. X. Xiang and H. J. Tian. The asymptotic stability of one-parameter methods for neutral differential equations. BIT, 1994, 34: 400-408
61. J. H. Park and S. Won. A note on stability of neutral delay-differential systems. Journal of the Franklin Institute, 1999, 336: 543-548
62. J. H. Park and S. Won. Asymptotic stability of neutral systems with multiple delays. Journal of Optimization Theory and Applications, 1999, 103: 187-200
63. E. N. Chukwu. Stability and time-optimal control of hereditary Systems, Academic Press, New York, 1992
64. T. J. Tarn, T. Yang, X. Zeng and C.Guo. Periodic output feedback stabilization of neutral systems. IEEE Transactions on Automatic Control, 1996, 41: 511-521