Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay

In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the on...

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Bibliographic Details
Published in:Applied mathematics and computation 2016-08, Vol.286, p.57-71
Main Authors: Nguyen, Minh Cuong, Trinh, Hieu
Format: Article
Language:English
Subjects:
Computational efficiency
Cost engineering
Design engineering
Dynamical systems
Linear matrix inequality (LMI)
Mathematical models
Nonlinear dynamics
Nonlinear systems
Nonlinearity
One-sided Lipschitz condition
Simultaneous estimation
State estimation
Time-delay
Unknown inputs
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Summary:In this paper, we address the problem of unknown input observer design, which simultaneously estimates state and unknown input, of a class of nonlinear discrete-time systems with time-delay. A novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one-sided Lipschitz and quadratically inner-bounded conditions is proposed. This approach also allows us to reconstruct the unknown inputs of the systems. The nonlinear system is first transformed to a new system which can be decomposed into unknown-input-free and unknown-input-dependent subsystems. The estimation problem is then reduced to designing observer for the unknown-input-free subsystem. Rather than full-order observer design, in this paper, we propose observer design of reduced-order which is more practical and cost effective. By utilizing several mathematical techniques, the time-delay issue as well as the bilinear terms, which often emerge when designing observers for nonlinear discrete-time systems, are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form. Two numerical examples are given to show the efficiency and high performance of our results.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2016.04.003