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Finite-time control for linear continuous system with norm-bounded disturbance. (English) Zbl 1221.93066
Summary: The definition of finite-time \(H_{\infty }\) control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

93B36 \(H^\infty\)-control
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[1] Zhou, K.; Khargonekar, P.P., An algebraic Riccati equation approach to \(H_\infty\) optimization, Syst control lett, 11, 85-91, (1988) · Zbl 0666.93025
[2] Doyle, J.C.; Glover, K.; Khargonekar, P.P.; Francis, B.A., State space solutions to standard \(H_2\) and \(H_\infty\) control problem, IEEE trans automat control, 34, 831-847, (1989) · Zbl 0698.93031
[3] Boyd, S.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequality in systems and control theory, SIAM studies in applied mathematics, SIAM, Philadelphia, (1994)
[4] Bhattacharyya, S.P.; Chapellat, H.; Keel, L.H., Robust control: the parametric approach, (1995), Prentice Hall PTR Upper Saddle River, NJ · Zbl 0838.93008
[5] Zhou, K.; Doyle, J.C., Essentials of robust control, (1998), Prentice Hall Upper Saddle River, NJ
[6] Song, S.H.; Kim, J.K., \(H_\infty\) control of discrete-time linear systems with norm-bounded uncertainties and time delay in state, Automatica, 34, 137-139, (1998) · Zbl 0904.93011
[7] Amato, F.; Ariola, M.; Dorate, P., Finite-time control of linear systems subject to parametric uncertainties and disturbances, Automatica, 37, 1459-1463, (2001) · Zbl 0983.93060
[8] Dorato P. Short time stability in linear time-varying systems. In: Proceeding of the IRE international convention record part 4; 1961. p. 83-7.
[9] Weiss, L.; Infante, E.F., Finite time stability under perturbing forces and on product spaces, IEEE trans automat control, 12, 54-59, (1967) · Zbl 0168.33903
[10] Amato, F.; Ariola, M.; Dorate, P., Finite-time stabilization via dynamic output feedback, Automatica, 42, 337-342, (2006) · Zbl 1099.93042
[11] Aamto, F.; Ariola, M., Finite-time control of discrete-time linear system, IEEE trans automat control, 50, 5, 724-729, (2005) · Zbl 1365.93182
[12] Feng, J.; Wu, Z.; Sun, J., Finite-time control of linear singular systems with parametric uncertainties and disturbances, Acta automatica sinica, 31, 4, 634-637, (2006)
[13] Shen, Y., Finite-time control for a class of linear discrete-time systems, Control decision, 23, 1, 107-109, (2008)
[14] Shen Y. Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance. Control Theory Appl, in press.
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