×

\(H_{\infty}\) output feedback control for uncertain stochastic systems with time-varying delays. (English) Zbl 1073.93022

Summary: This paper deals with the problem of \(H_{\infty}\) output feedback control for uncertain stochastic systems with time-varying delays. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is the design of a full-order dynamic output feedback controller ensuring robust exponential mean-square stability and a prescribed \(H_{\infty}\) performance level for the resulting closed-loop system, irrespective of the uncertainties. A sufficient condition for the existence of such an output feedback controller is obtained and the expression of desired controllers is given.

MSC:

93B36 \(H^\infty\)-control
93C23 Control/observation systems governed by functional-differential equations
93E15 Stochastic stability in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, SIAM studies in applied mathematics (1994), SIAM: SIAM Philadelphia PA
[2] Choi, H. H.; Chung, M. J., Observer-based \(H_\infty\) controller design for state delayed linear systems, Automatica, 32, 1073-1075 (1996) · Zbl 0850.93215
[3] Choi, H. H.; Chung, M. J., Robust observer-based \(H_\infty\) controller design for linear uncertain time-delay systems, Automatica, 33, 1749-1752 (1997) · Zbl 1422.93062
[4] El Bouhtouri, A.; Hinrichsen, D.; Pritchard, A. J., \(H^\infty \)-type control for discrete-time stochastic systems, International Journal of Robust and Nonlinear Control, 9, 923-948 (1999) · Zbl 0934.93022
[5] Esfahani, S. H.; Petersen, I. R., An LMI approach to output-feedback-guaranteed cost control for uncertain time-delay systems, International Journal of Robust and Nonlinear Control, 10, 157-174 (2000) · Zbl 0951.93032
[6] Fukuda, M.; Kojima, M., Branch-and-cut algorithms for the bilinear matrix inequality eigenvalue problem, Computational Optimization and Applications, 19, 79-105 (2001) · Zbl 0979.65051
[7] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to \(H_\infty\) control, International Journal of Robust and Nonlinear Control, 4, 421-448 (1994) · Zbl 0808.93024
[8] Hinrichsen, D.; Pritchard, A. J., Stochastic \(H^\infty \), SIAM Journal on Control Optimization, 36, 1504-1538 (1998) · Zbl 0914.93019
[9] Jeung, E. T.; Kim, J. H.; Park, H. B., \(H_\infty \)-output feedback controller design for linear systems with time-varying delayed state, IEEE Transaction of Automatic Control, 43, 971-974 (1998) · Zbl 0952.93032
[10] Kolmanovskii, V. B.; Myshkis, A. D., Introduction to the theory and applications of functional differential equations (1999), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0907.39012
[11] Lee, J. H.; Kim, S. W.; Kwon, W. H., Memoryless \(H_\infty\) controllers for state delayed systems, IEEE Transaction of Automatic Control, 39, 159-162 (1994) · Zbl 0796.93026
[12] Mao, X., Stochastic differential equations and their applications (1997), Horwood: Horwood Chichester
[13] Tuan, H. D.; Apkarian, P., Low nonconvexity-rank bilinear matrix inequalitiesAlgorithms and applications in robust controller and structure designs, IEEE Transaction of Automatic Control, 45, 2111-2117 (2000) · Zbl 0989.93036
[14] Wonham, W. M., On a matrix Riccati equation of stochastic control, SIAM Journal on Control, 6, 681-697 (1968) · Zbl 0182.20803
[15] Xu, S.; Chen, T., Robust \(H_\infty\) control for uncertain stochastic systems with state delay, IEEE Transaction of Automatic Control, 47, 2089-2094 (2002) · Zbl 1364.93755
[16] Xu, S.; Lam, J.; Yang, C., \(H_\infty\) and positive real control for linear neutral delay systems, IEEE Transaction of Automatic Control, 46, 1321-1326 (2001) · Zbl 1008.93033
[17] Xu, S.; Lam, J.; Yang, C., Robust \(H_\infty\) control for uncertain linear neutral delay systems, Optimal Control Application and Methods, 23, 113-123 (2002) · Zbl 1072.93506
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.