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Robust stabilization for a class of discrete-time nonlinear systems via output feedback: The unified LMI approach. (English) Zbl 1026.93048
The paper focuses on sufficient convex linear matrix inequality (LMI) formulations of the stability analysis and controller design problems for a linear discrete-time system affected by nonlinear additive perturbations. It is assumed that the nonlinear perturbation is bounded by a given quadratic function of the system state and input. An elegant LMI formulation is provided for analyzing stability in the presence of such nonlinearities (necessary and sufficient LMI condition of Lemma 2), and then it is extended throughout the paper in a routine manner to static-output feedback design (sufficient LMI condition of Theorem 1), dynamic output feedback design (sufficient LMI condition of Theorem 3), as well as a decentralized controller design. The paper is reasonably well written, and can be considered as a minor extension of existing results for continuous-time systems or less general nonlinearities. A discussion on how conservative (pessimistic) the sufficient LMI conditions can be is missing however, in particular concerning the use of the restrictive equality constraint $$CQ=ZC$$ in the static output feedback condition of Theorem 1.

##### MSC:
 93D21 Adaptive or robust stabilization 93C55 Discrete-time control/observation systems 93C10 Nonlinear systems in control theory 15A39 Linear inequalities of matrices 93C73 Perturbations in control/observation systems
LMI toolbox
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