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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.

##### MSC:
 93B36 $H^\infty$-control
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##### References:
 [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 · doi:10.1016/0167-6911(88)90080-1 [2] Doyle, J. C.; Glover, K.; Khargonekar, P. P.; Francis, B. A.: State space solutions to standard H2 and H$\infty$ control problem, IEEE trans automat control 34, 831-847 (1989) · Zbl 0698.93031 · doi:10.1109/9.29425 [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) · Zbl 0816.93004 [4] Bhattacharyya, S. P.; Chapellat, H.; Keel, L. H.: Robust control: the parametric approach, (1995) · Zbl 0838.93008 · http://www.prenhall.com/ [5] Zhou, K.; Doyle, J. C.: Essentials of robust control, (1998) · Zbl 0890.93003 [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 · doi:10.1016/S0005-1098(97)00182-9 [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 · doi:10.1016/S0005-1098(01)00087-5 [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 · doi:10.1016/j.automatica.2005.09.007 [11] Aamto, F.; Ariola, M.: Finite-time control of discrete-time linear system, IEEE trans automat control 50, No. 5, 724-729 (2005) [12] Feng, J.; Wu, Z.; Sun, J.: Finite-time control of linear singular systems with parametric uncertainties and disturbances, Acta automatica sinica 31, No. 4, 634-637 (2006) [13] Shen, Y.: Finite-time control for a class of linear discrete-time systems, Control decision 23, No. 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.