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Robust analysis and synthesis of linear time-delay systems with norm-bounded time-varying uncertainty. (English) Zbl 0875.93110

Summary: The problems of robust analysis and synthesis of systems with state-delay and norm-bounded time-varying parameter uncertainty are studied. It is shown that these problems are equivalent to the \(H_{\infty}\) analysis and synthesis problems of an auxiliary system, which is independent of the time-delay and the uncertainty in the system. The necessary and sufficient conditions for the equivalence are developed. Thus any standard \(H_{\infty}\) analysis and synthesis method can be used to solve this problem.

MSC:

93B36 \(H^\infty\)-control
34K35 Control problems for functional-differential equations

Software:

LMI toolbox
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Full Text: DOI

References:

[1] Barmish, B. R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system, J. Optim. Theory Appl., 46, 399-408 (1985) · Zbl 0549.93045
[2] Boyd, S.; EI Ghaoui, L.; Feron, E.; Balakrishnam, V., Linear Matrix Inequalities in Systems and Control Theory (1994), SIAM: SIAM Philadelphia
[3] Doyle, J. C.; Glove, K.; Khargonekar, P. P.; Francis, B. A., State space solution to standard \(H_2\) and \(H_∞\) problems, IEEE Trans. Automat. Control, AC-34, 831-847 (1989) · Zbl 0698.93031
[4] Francis, B. A., A Course in \(H_∞\) Control Theory (1987), Springer: Springer New York · Zbl 0624.93003
[5] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to \(H_∞\) control, Int. J. Robust Nonlinear Control, 4, 421-448 (1994) · Zbl 0808.93024
[6] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., The LMI control toolbox (1995), The MathWorks, Inc
[7] Garcia, G.; Bernussou, J.; Arzelier, D., Robust stabilization of discrete time linear systems with norm-bounded time-varying uncertainty, Systems Control Lett., 22, 327-339 (1994) · Zbl 0820.93059
[8] Gu, K., \(H_∞\) control of systems under bounded uncertainties in all system matrices, IEEE Trans. Automat. Control, AC-39, 1320-1322 (1994) · Zbl 0812.93029
[9] Khargonekar, P. P.; Petersen, I. R.; Rotea, M. A., \(H_∞\) optimal control with state feed back, IEEE Trans. Automat. Control, AC-33, 786-788 (1988) · Zbl 0655.93026
[10] Khargonekar, P. P.; Petersen, I. R.; Zhou, K., Robust stabilization of uncertain linear system: quadratic stabilizability and \(H_∞\) control theory, IEEE Trans. Automat. Control, AC-35, 356-361 (1990) · Zbl 0707.93060
[11] Lee, J. H.; Kim, S. W.; Kwon, W. H., Memoryless \(H_∞\) controllers for stable delay systems, IEEE Trans. Automat. Control, AC-39, 156-162 (1994)
[12] Lou, J. S.; Johnson, A.; Van Den Bosch, P. P.J., Delay-independent robust stability of uncertain linear system, Systems Control Lett., 24, 33-39 (1995) · Zbl 0877.93078
[13] Mahmoold, M. S.; Al-Muthairi, N. F., Design of a robust controller for time-delay systems, IEEE Trans. Automat. Control, AC-39, 995-999 (1994) · Zbl 0807.93049
[14] Mahmoold, M. S.; Al-Muthairi, N. F., Quadratic stabilization of continuous time systems with state delay and norm bounded time varying uncertainties, IEEE Trans. Automat. Control, AC-39, 2135-2139 (1994) · Zbl 0925.93585
[15] Petersen, I. R.; Hollot, C. V., A Riccati equation approach to the stabilization of uncertain linear system, Automatica, 22, 397-411 (1986) · Zbl 0602.93055
[16] Sampei, T.; Mita, T.; Nakamichi, M., An algebraic approach to the \(H_∞\) output feedback control problem, Systems Control Lett., 14, 13-24 (1990) · Zbl 0692.93031
[17] Shen, J. C.; Chen, B. S.; Kung, F. C., Memoryless \(H_∞\) controllers for stable delay systems, IEEE Trans. Automat. Control, AC-38, 638-640 (1993)
[18] Su, T. J.; Lie, P. L., Robust stability for linear uncertain time-delay system with delay dependence, Int. J. System Sci., 24, 1067-1080 (1993) · Zbl 0773.93070
[19] Thhowsen, T., Uniform ultimate boundedness of the solutions of uncertain dynamic delay systems with state dependent and memoryless feedback control, Int. J. Control, 45, 1135-1143 (1983) · Zbl 0511.93052
[20] Trinh, H.; Aldeen, M., Stabilization of uncertain dynamic delay systems by memoryless feedback controllers, Int. J. Control, 59, 1525-1542 (1994) · Zbl 0806.93050
[21] Tseng, C. L.; Fong, I. K.; Su, J. H., Robust stability analysis for uncertain delay system with output feedback controller, Systems Control Lett., 14, 13-24 (1990)
[22] Xie, L.; Fu, M.; DeSouza, C. E., \(H_∞\) control and quadrative stabilization of system with parameter uncertain via output feedback, IEEE Trans. Automat. Control, AC-37, 1253-1256 (1992) · Zbl 0764.93067
[23] Xie, L.; DeSouza, C. E., Robust \(H_∞\) control for linear systems with norm-bounded time-varying uncertainty, IEEE Trans. Automat. Control, AC-37, 1188-1191 (1992) · Zbl 0764.93027
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