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Finite-time control of discrete-time linear systems: analysis and design conditions. (English) Zbl 1191.93099

Summary: We deal with some finite-time control problems for discrete-time, time-varying linear systems. First we provide necessary and sufficient conditions for finite-time stability; these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference Lyapunov inequality. Then we address the design problem. The proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite-time sense; all these conditions can be expressed in terms of LMIs and therefore are numerically tractable, as shown in the example included in the paper.

MSC:

93C55 Discrete-time control/observation systems
93C05 Linear systems in control theory
93D20 Asymptotic stability in control theory
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[2] Amato, F.; Ariola, M., Finite-time control of discrete-time linear systems, IEEE Transactions on Automatic Control, 50, 724-729 (2005) · Zbl 1365.93182
[4] Amato, F.; Ariola, M.; Cosentino, C., Finite-time stabilization via dynamic output feedback, Automatica, 42, 337-342 (2006) · Zbl 1099.93042
[6] Amato, F.; Ariola, M.; Dorato, P., Finite-time control of linear systems subject to parametric uncertainities and disturbances, Automatica, 37, 9, 1459-1463 (2001) · Zbl 0983.93060
[7] Ambrosino, R.; Calabrese, F.; Cosentino, C.; De Tommasi, G., Sufficient conditions for finite-time stability of impulsive dynamical systems, IEEE Transactions on Automatic Control, 54, 861-865 (2009) · Zbl 1367.93425
[8] Boyd, S.; Ghaoui, L. E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory (1994), SIAM Press · Zbl 0816.93004
[10] Gahinet, P., Explicit controller formulas for LMI-based \(H_\infty\) synthesis, Automatica, 32, 1007-1014 (1996) · Zbl 0855.93025
[11] Garcia, G.; Tarbouriech, S.; Bernussou, J., Finite-time stabilization of linear time-varying continuous systems, IEEE Transactions on Automatic Control, 54, 364-369 (2009) · Zbl 1367.93060
[12] Packard, A.; Balas, G.; Safonov, M.; Chiang, R.; Gahinet, P.; Nemirovski, A., Robust control toolbox (1984-2006), The Mathworks Inc.: The Mathworks Inc. Natick, MA
[13] Weiss, L.; Infante, E. F., Finite time stability under perturbing forces and on product spaces, IEEE Transactions on Automatic Control, 12, 54-59 (1967) · Zbl 0168.33903
[14] Zhao, S.; Sun, J.; Liu, L., Finite-time stability of linear time-varying singular systems with impulsive effects, International Journal of Control, 81, 11, 1824-1829 (2008) · Zbl 1148.93345
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