Novel LMI conditions for observer-based stabilization of Lipschitzian nonlinear systems and uncertain linear systems in discrete-time

Salim Ibrir 1, * Sette Diop 2
* Corresponding author
2 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : In this paper, it is shown that the observer-based control of uncertain discrete-time linear systems is conditioned by the solvability of three linear matrix inequalities that must hold simultaneously. The developed theory is then extended to Lipschitz discrete-time nonlinear systems. We show that the observer-based control problem, which is originally a non-convex issue, can be decomposed into two separate convex problems formulated as a set of numerically tractable linear matrix inequalities conditions. The new proposed linear matrix inequalities are neither iterative nor subject to any equality constraint. Illustrative examples are given to indicate the novelty and effectiveness of the proposed design.
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Submitted on : Wednesday, June 5, 2013 - 5:28:14 PM
Last modification on : Thursday, April 5, 2018 - 12:30:23 PM

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Salim Ibrir, Sette Diop. Novel LMI conditions for observer-based stabilization of Lipschitzian nonlinear systems and uncertain linear systems in discrete-time. Applied Mathematics and Computation, Elsevier, 2008, 206 (2), pp.579. ⟨10.1016/j.amc.2008.05.150⟩. ⟨hal-00830851⟩

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