Stochastic finite-time stabilization for uncertain jump systems via state feedback

Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME

Volumn 132, Issue 3, 2010, Pages 1-4

  He, Shuping ^a   Liu, Fei ^a  

^a JIANGNAN UNIVERSITY   (China)

Author keywords

Linear matrix inequalities; Markov jump systems (MJSs); Stochastic finite time bounded; Stochastic finite time stabilization; Uncertain

Indexed keywords

EXTERNAL DISTURBANCES; FINITE TIME STABILIZATION; FINITE-STATE; JUMP SYSTEM; JUMPING PARAMETERS; LYAPUNOV-KRASOVSKII FUNCTIONALS; MARKOV JUMP SYSTEM; MARKOV JUMP SYSTEMS (MJSS); SIMULATION RESULT; STABILIZATION CRITERIA; STOCHASTIC FINITE-TIME BOUNDED; SUFFICIENT CONDITIONS; UNCERTAIN; UNCERTAIN PARAMETERS;

CONTROLLERS; FEEDBACK; LYAPUNOV FUNCTIONS; MARKOV PROCESSES; NONLINEAR CONTROL SYSTEMS; STABILIZATION; STATE FEEDBACK; STOCHASTIC SYSTEMS; SWITCHING SYSTEMS; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

LINEAR MATRIX INEQUALITIES;

EID: 77955784882     PISSN: 00220434     EISSN: 15289028     Source Type: Journal    
DOI: 10.1115/1.4001278     Document Type: Article

References (22)

1. Amato, F., Ariola, M., and Dorato, P., 2001, "Finite-Time Control of Linear Systems Subject to Parametric Uncertainties and Disturbances," Automatica, 37(9), pp. 1459-1463.
2. Dorato, P., 1961, "Short Time Stability in Linear Time-Varying Systems," Proceedings of the IRE international Convention Record, New York, Part 4, pp. 83-87.
3. Weiss, L., and Infante, E. F., 1967, "Finite Time Stability Under Perturbing Forces and on Product Spaces," IEEE Trans. Autom. Control, 12(1), pp. 54-59.
4. Amato, F., Ariola, M., Abdallah, C. T., and Dorato, P., 1999, "Dynamic Output Feedback Finite-Time Control of LTI Systems Subject to Parametric Uncertainties and Disturbances," Proceedings of the European Control Conference, Springer, Berlin, pp. 1176-1180.
5. Boyd, S. P., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, Linear Matrix Inequalities in System and Control Theory. Society for Industrial and Applied Mathematics, Academic, Philadelphia.
6. Amato, F., and Ariola, M., 2005, "Finite-Time Control of Discrete-Time Linear Systems," IEEE Trans. Autom. Control, 50(5), pp. 724-729.
7. Amato, F., Ariola, M., and Cosentino, C., 2006, "Finite-Time Stabilization via Dynamic Output Feedback," Automatica, 42(2), pp. 337-342.
8. Krasovskii, N. M., and Lidskii, E. A., 1961, "Analytical Design of Controllers in Systems With Random Attributes," Autom. Remote Control (Engl. Transl.), 22 (1-3), pp. 1021-1025.
9. Krasovskii, N. M., and Lidskii, E. A., 1961, "Analytical Design of Controllers in Systems With Random Attributes," Autom. Remote Control (Engl. Transl.), 22 (1-3), pp. 1141-1146.
10. Krasovskii, N. M., and Lidskii, E. A., 1961, "Analytical Design of Controllers in Systems With Random Attributes," Autom. Remote Control (Engl. Transl.), 22(1-3), pp. 1289-1294.
11. Blair, W. P., and Sworder, D. D., 1975, "Feedback Control of a Class of Linear Discrete Systems With Jump Parameters and Quadratic Cost Criteria," Int. J. Control, 21, pp. 833-841.
12. Sworder, D. D., and Rogers, R. O., 1983, "An LQG Solution to a Control Problem With Solar Thermal Receiver," IEEE Trans. Autom. Control, 28, pp. 971-978.
13. Athans, M., 1987, "Command and Control Theory: A Challenge to Control Science," IEEE Trans. Autom. Control, 32, pp. 286-293.
14. Aaawinchaichote, W., Nguang, S. K., and Shi, P., 2007, "Robust H∞ Fuzzy Filter Design for Uncertain Nonlinear Singularly Perturbed Systems With Markovian Jumps: An LMI Approach," Inf. Sci. (N. Y.), 177, pp. 1699-1714.
15. Feng, X., Loparo, K. A., and Ji, Y., 1992, "Stochastic Stability Properties of Jump Linear Systems," IEEE Trans. Autom. Control, 37, pp. 38-53.
16. Boukas, E. K., and Benjelloun, K., 2001, "On Stabilization of Uncertain Linear Systems With Jump Parameters," Int. J. Control, 72, pp. 842-850.
17. Rami, M. A., and El Ghaoui, L., 1994, "Robust Stabilization of Jump Linear Systems Using Linear Matrix Inequalities," Proceedings of IFAC Symposium on Robust Control Design, Rio de Janeiro, Brazil, pp. 148-151.
18. Ji, Y., and Chizeck, H. J., 1990, "Controllability, Stability and Continuous Time Markov jump Linear Quadratic Control," IEEE Trans. Autom. Control, 35(7), pp. 777-788.
19. el Ghaoui, L., and Ait Rami, M., 1996, "Robust Stabilization of Jump Linear Systems Using Linear Matrix Inequalities," Int. J. Robust Nonlinear Control, 6(9-10), pp. 1015-1022.
20. Ait Rami, M., and El Ghaoui, L., 1995, "H∞ State-Feedback Control of Jump Linear Systems," Proceedings of the 34th IEEE Conference on Decision and Control, Vol. 1, pp. 951-952.
21. He, S., and Liu, F., 2008, "Unbiased H∞ Filtering for Neutral Markov Jump Systems," Appl. Math. Comput., 206(1), pp. 175-185.
22. Wang, Y., Xie, L., and de Souza, C. E., 1992, "Robust Control of a Class of Uncertain Nonlinear Systems," Syst. Control Lett., 19, pp. 139-149.