Geodesic
On finite time stability with guaranteed cost control of uncertain linear systems
Kybernetika, Tome 54 (2018) no. 5, pp. 1071-1090.

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This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction of the proposed robust control law. In particular, the construction of the feedback control law is brought back to a feasibility problem which can be solved inside the convex optimization framework. The effectiveness of the proposed approach is shown by means of the results obtained on a numerical and a physical example.
DOI : 10.14736/kyb-2018-5-1071
Classification : 93B50, 93B51, 93D15
Keywords: differential LMIs; finite time stability; guaranteed cost control; robust control; state feedback control 
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     title = {On finite time stability with guaranteed cost control of uncertain linear systems},
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Qayyum, Atif; Pironti, Alfredo. On finite time stability with guaranteed cost control of uncertain linear systems. Kybernetika, Tome 54 (2018) no. 5, pp. 1071-1090. doi : 10.14736/kyb-2018-5-1071. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-5-1071/

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