Robust and resilient finite-time bounded control of discrete-time uncertain nonlinear systems

Finite-time state-feedback stabilization is addressed for a class of discrete-time nonlinear systems with conic-type nonlinearities, bounded feedback control gain perturbations, and additive disturbances. First, conditions for the existence of a robust and resilient linear state-feedback controller...

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Bibliographic Details
Published in:Automatica (Oxford) 2013-07, Vol.49 (7), p.2292-2296
Main Authors: ElBsat, Mohammad N., Yaz, Edwin E.
Format: Article
Language:English
Subjects:
Adaptative systems
Applied sciences
Computer science
control theory
systems
Control system analysis
Control system synthesis
Control systems
Control theory. Systems
Discrete-time systems
Disturbances
Dynamical systems
Exact sciences and technology
Finite-time stability
Gain
Hyperspheres
LMIs
Nonlinear dynamics
Nonlinear systems
Nonlinearity
Perturbation methods
Robust Control
State-feedback
System theory
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Summary:Finite-time state-feedback stabilization is addressed for a class of discrete-time nonlinear systems with conic-type nonlinearities, bounded feedback control gain perturbations, and additive disturbances. First, conditions for the existence of a robust and resilient linear state-feedback controller for this class of systems are derived. Then, using linear matrix inequality techniques, a solution for the controller gain and the maximum allowable bound on the gain perturbation is obtained. The developed controller is robust for all unknown nonlinearities lying in a known hypersphere with an uncertain center and all admissible disturbances. Moreover, it is resilient against any bounded perturbations that may alter the controller’s gain by at most a prescribed amount. The paper is concluded with a numerical example showcasing the applicability of the main result.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.04.003