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Robust \(H_\infty\) control for a generic linear rational expectations model of economy. (English) Zbl 1193.93092
Summary: Large time-delay and small disturbance attenuation are very important for macroeconomic systems. This paper is concerned with the problem of robust \(H_\infty\) control with large time-delay and small disturbance attenuation for a generic linear rational expectations model of economy with uncertainties, time-varying delay and random shocks. The norm bounded uncertainties are used to describe the uncertainties of economic system. The concept of two levels of conservatism and the approach of Parameters Weak Coupling Linear Matrix Inequalities (PWCLMIs) are developed in this paper. The result is presented in terms of PWCLMIs in this note. Large time-delay and small disturbance attenuation are achieved without increasing conservatism of result. Furthermore, according to the robust \(H_\infty\) result, one will obtain various results readily by employing different games. An example is given to show the benefit of the presented approach.

93B35 Sensitivity (robustness)
91B74 Economic models of real-world systems (e.g., electricity markets, etc.)
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations
Full Text: DOI
[1] Hansen, L.P.; Sargent, T.J., Robustness, (2007), Princeton University Press
[2] Gilboa, I.; Schmeidler, D., Maxmin expected utility with non-unique prior, J. math. econ., 18, 141-153, (1989) · Zbl 0675.90012
[3] Epstein, L.G.; Schneider, M., Recursive multiple-priors, J. econ. theory, 113, 1-31, (2003) · Zbl 1107.91360
[4] Hansen, L.P.; Sargent, T.J.; Turmuhambetova, G.; Williams, N., Robust control and model misspecification, J. econ. theory, 128, 45-90, (2006) · Zbl 1152.93356
[5] Williams, N., Robust control. an entry for the new palgrave, (2007), Princeton University Press
[6] Giordani, P.; Söderlind, P., Solution of macromodels with hansen – sargent robust policies: some extensions, J. econ. dynam. control, 28, 2367-2397, (2004) · Zbl 1202.91222
[7] Tetlow, R.J.; von zur Muehlen, P., Robust monetary policy with misspecified models: does model uncertainty always call for attenuated policy?, J. econ. dynam. control, 25, 911-949, (2001) · Zbl 0978.91067
[8] Kasa, K., Model uncertainty, robust policies, and the value of commitment, Macroecon. dynam., 6, 145-166, (2002) · Zbl 1006.93019
[9] Giannoni, M.P., Does model uncertainty justify caution? robust optimal monetary policy in a forward-looking model, Macroecon. dynam., 6, 111-144, (2002) · Zbl 1008.91085
[10] Kendrick, D.A., Stochastic control for economic models: past, present and the paths ahead, J. econ. dynam. control, 29, 3-30, (2005) · Zbl 1202.93173
[11] Andrea, C.; Francesca, P.; Rodolfo, S.-S., Water reservoir control under economic, social and environmental, Automatica, 44, 1595-1607, (2008) · Zbl 1283.93250
[12] Wu, Z.; Su, H.; Chu, J.; Zhou, W., Improved result on stability analysis of discrete stochastic neural networks with time delay, Phys. lett. A, 373, 1546-1552, (2009) · Zbl 1228.92004
[13] Zhou, W.; Li, M., Mixed time-delays dependent exponential stability for uncertain stochastic high-order neural networks, Appl. math. comput., 215, 503-513, (2009) · Zbl 1206.65025
[14] Wang, H.; Xue, A.; Lu, R., Absolute stability criteria for a class of nonlinear singular systems with time delay, Nonlinear anal. theory method appl., 70, 621-630, (2009) · Zbl 1168.34048
[15] Lu, R.; Dai, X.; Su, H.; Chu, J.; Xue, A., Delay-dependant robust stability and stabilization conditions for a class of lur’e singular time-delay systems, Asian J. control, 10, 462-469, (2009)
[16] Xu, S.; Chen, T., \(H_\infty\) output feedback control for uncertain stochastic systems with time-varying delays, Automatica, 40, 2091-2098, (2004) · Zbl 1073.93022
[17] Wu, Z.; Zhou, W., Delay-dependent robust \(H_\infty\) control for uncertain singular time-delay systems, IET control theory appl., 5, 1234-1241, (2007)
[18] Yue, D.; Han, Q.-L., Delay-dependent exponential stability of stochastic systems with time-varying delay, nonlinearity, and Markovian switching, IEEE trans. automat. control, 50, 217-222, (2005) · Zbl 1365.93377
[19] Luenberger, D.G., Introduction to dynamic systems: theory, models, and applications, (1979), John Wiley and Sons Inc. New York · Zbl 0458.93001
[20] C.-H. Fan, Y.-M. Zhang, The time delay and oscillation of economic system, in: Proceedings of the 1986 International Conference of the System Dynamics Society, SEVILLA, 1986, pp. 525-535.
[21] N.D. Kondratiev, The Major Economic Cycles (in Russian), Moscow, 1925.
[22] M. Li, W. Zhou, H. Wang, Y. Chen, R. Lu, H. Lu, Delay-dependent robust \(H_\infty\) control for uncertain stochastic systems, in: Proceedings of the 17th World Congress of the International Federation of Automatic Control, Seoul, Korea, 2008, pp. 6004-6009.
[23] L. Jiang, J. Fang, W. Zhou, D. Zheng, H. Lu, Stability of economic input – output model, in: Proceedings of the 27th Chinese Control Conference, Kunming, China, 2008, pp. 804-807.
[24] L. Jiang, J. Fang, W. Zhou, Stability analysis of economic discrete-time singular dynamic input – output model, in: Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, Kunming, China, 2008, pp. 1434-1438.
[25] Wang, Z.; Lauria, S.; Fang, J.; Liu, X., Exponential stability of uncertain stochastic neural networks with mixed time-delays, Chaos, solitons fractals, 32, 62-72, (2007) · Zbl 1152.34058
[26] Xie, L.; de Souza, C.E., Robust \(h_\infty\) control for linear systems with norm-bounded time-varying uncertainties, IEEE trans. automat. control, 14, 1188-1191, (1992) · Zbl 0764.93027
[27] Tang, B.; Cheng, C.; Zhong, M., Theory and applications of robust economic control, (2000), China Textile University Press Shanghai
[28] Parthasarathy, T.; Raghavan, T.E.S., Some topics in two-person games, SIAM rev., 14, 356-357, (1972) · Zbl 0225.90049
[29] F. Gouaisbaut, D. Peaucelle, A note on stability of time delay systems, in: D. Arzelier, D. Henrion (Eds.), The Fifth IFAC Symposium on Robust Control Design, vol. 5(1), Toulouse, France, 2006. · Zbl 1293.93589
[30] Xu, S.; Lam, J., On equivalence and efficiency of certain stability criteria for time-delay systems, IEEE trans. automat. control, 52, 95-101, (2007) · Zbl 1366.93451
[31] Xu, S.; Lam, J., A survey of linear matrix inequality techniques in stability analysis of delay systems, Int. J. syst. sci., 39, 1095-1113, (2008) · Zbl 1156.93382
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