Abstract
This paper deals with the problem of robust and reliable H ∞ control design for linear uncertain time-delay systems with time-varying norm-bounded parameter uncertainty, and also with actuator failures among a specified subset of actuators. A state feedback control design is presented that stabilizes the plant and guarantees an H ∞-norm bound constraint on attenuation of the augmented disturbances, including failure signals, for all admissible uncertainties as well as actuator failures. It is shown that the existence of the desired controllers is related to the positive definite solution of a parameter-dependent Riccati-like matrix equation, whose solving algorithm is also discussed in detail. Two illustrative examples are provided to demonstrate the applicability of the proposed method.
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References
T. Amemiya and G. Leitmann, A method for designing a stabilizing control for a class of uncertain linear delay systems. Dynam. Control 4(1994), 147–167.
H. H. Choi and M. J. Chung, Observer-based H8controller design for state delayed linear systems. Automatica 32(1996), 1073–1075.
____, An LMI approach to H8controller design for linear time-delay systems. Automatica 33(1997), 737–739.
I. Derese, and E. Noldus, Design of linear feedback laws for bilinear systems. Int. J. Control 31(1980), 219–237.
J. C. Doyle, K. Glover, P. P. Khargonekar, and B. A. Francis, Statespace solutions to the standard H2 and H8control problems. IEEE Trans. Automat. Control 34 ( 1989 ). 831–847 .
C. Foias, A. Tannenbaum, and G. Zames, On the H8-optimal sensitivity problem for systems with delays. SIAM J. Control Optim. 25(1987), 686–705.
J. Ge, P. M. Frank, and C.-F. Lin, Robust H8state feedback control for linear systems with state delay and parameter uncertainty. Automatica 32(1996), 1183–1185.
____, Design of reliable controllers for state delayed systems. Eur. J. Control 2(1996), 239–248.
K. Gu, H8control of systems under norm bounded uncertainties in all system matrices. IEEE Trans. Automat. Control 39(1994), 1320–1322.
I. K. Hale, S. M. Verduyn Lunel, Introduction to functional differential equations. Appl. Math. Sci. 99, Springer-Verlag(1993).
P. P. Khargonekar, I. R. Petersen, and K. Zhou, Robust stabilization of uncertain linear systems: quadratic stabilization and H8control theory. IEEE Trans. Automat. Control 35(1990), 356–361.
V. Kolmanovskii and L. Shaikhet, Matrix Riccati equations and stability of stochastic linear systems with nonincreasing delays. Funct. Differ. Equations 4(1997), 279–293.
J. H. Lee, S. W. Kim, and W. H. Kwon, Memoryless H8controllers for state delayed systems. IEEE Trans. Automat. Control 39(1994), 159–162.
M. S. Mahmoud and N. F. Al-Muthairi, Quadratic stabilization of continuous systems with state-delay and norm-bounded time-varying uncertainties. IEEE Trans. Automat. Control 39(1994), 2135–2139.
M. Malek-Zavarei and M. Jamshidi, Time-delay systems: analysis, optimization, and application. North-Holland, Amsterdam (1987).
M. Mariton and P. Bertrand, Improved multiplex control systems: Dynamic reliability and stochastic optimality. Int. J. Control 44(1986), 219–234.
C.-J. Seo and B. K. Kim, Robust and reliable H8control for linear systems with parameter uncertainty and actuator failure. Automatica 32(1997), 465–467.
J. C. Shen, B. S. Chen, and F. C. Kung, Memoryless stabilization of uncertain dynamic delay systems: Riccati equation approach. IEEE Trans. Automat. Control 39(1994), 638–640.
D. D. Siljak, Reliable control using multiple control systems. Int. J. Control 31(1980), 303–329.
C. E. de Souza, M. Fu, and L. Xie, H8analysis and synthesis of discrete-time systems with time-varying uncertainty. IEEE Trans. Automat. Control 38(1993), 459–462.
H. Trinh and M. Aldeen, Stabilization of uncertain dynamic delay systems by memoryless feedback controller. Int. J. Control 59(1994). 1525–1542.
R. J. Veillette, Reliable state feedback and reliable observers. Proc. 31 IEEE Conf. on Decision and Control, Tucson, AZ (1992), 2898–2903.
R. J. Veillette, J. V. Medanic, and W. R. Perkins, Design of reliable control systems. IEEE Trans. Automat. Contro l 37(1992), 290–304.
Y. Wang, L. Xie, and C. E. de Souza, Robust control of a class of uncertain nonlinear systems. Systems Control. Lett. 19(1992), 139–149.
Z. Wang, B. Huang, and K. J. Burnham, Stochastic reliable control of a class of uncertain time-delay systems with unknown nonlinearities. IEEE Trans. Circuits and Systems I 48(2001), 646–650.
Z. Wang, B. Huang, and H. Unbehauen, Robust reliable control for a class of uncertain nonlinear state delayed systems. Automatica 35(1999), 955–963.
Z. Wang, X. Sun, J. Sun, and Z. Wang, Robust fault-tolerant control and design for uncertain linear systems. Acta Aeronautica et Astronautica 17(1996), 112–115 (in Chinese).
L. Xie, Output feedback H8control of systems with parameter uncertainty. Int. J. Contr. 63(1996), 741–750.
L. Xie and Y. C. Soh, Robust Kalman filtering for uncertain systems. Systems Control Lett. 22(1994), 123–129.
____, Robust control of linear systems with generalized positive real uncertainty. Automatica 33(1997), 963–967.
L. Xie and C. E. de Souza, Robust H8control for a class of uncertain linear time-invariant systems. IEEE Proc. Control Theory Appl. 138(1991), 479–483.
____, Robust H8control for linear systems with norm-bounded timevarying uncertainty. IEEE Trans. Automat. Control 37(1992), 1188–1191.
G. Zames, Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms, and approximate inverses. IEEE Trans. Automat. Control 26(1981), 301–320.
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Wang, Z., Qiao, H. H ∞ Reliable Control of Uncertain Linear State Delayed Systems. Journal of Dynamical and Control Systems 10, 55–76 (2004). https://doi.org/10.1023/B:JODS.0000012017.28986.1c
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DOI: https://doi.org/10.1023/B:JODS.0000012017.28986.1c