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Copyright © 2015 Sohaira Ahmad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper presents a novel nonlinear observer-design approach to one-sided Lipschitz nonlinear systems in the presence of output delays. The crux of the approach is to overcome the practical consequences of time delays, encountered due to distant sensor position and time lag in measurement, for estimation of physical and engineering nonlinear system states. A Lyapunov-Krasovskii functional is employed, the time derivative of which is solved using Jensen's inequality, one-sided Lipschitz condition, and quadratic inner-boundedness, and, accordingly, design conditions for delay-range-dependent nonlinear observer for delayed one-sided Lipschitz systems are derived. Further, novel solutions to the problems of delay-dependent observer synthesis of one-sided Lipschitz models and delay-range-dependent state estimation of linear and Lipschitz nonlinear systems are deduced from the present delay-range-dependent technique. An observer formulation methodology for retrieval of one-sided Lipschitz nonlinear-system states, which is robust against [subscript]L2[/subscript] norm-bounded perturbations, is devised. The resultant design conditions, in contrast to the conventional procedures, can be solved via less conservative linear matrix inequality- (LMI-) based routines that succeed by virtue of additional LMI variables, meaningful transformations, and cone complementary linearization algorithm. Numerical examples are worked out to illustrate the effectiveness of the proposed observer-synthesis approach for delayed one-sided Lipschitz systems.

Details

Title
Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays
Author
Sohaira Ahmad; Majeed, Raafia; Hong, Keum-Shik; Rehan, Muhammad
Publication year
2015
Publication date
2015
Publisher
John Wiley & Sons, Inc.
ISSN
1024123X
e-ISSN
15635147
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1667317099
Copyright
Copyright © 2015 Sohaira Ahmad et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.