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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