Observer Design for One-Sided Lipschitz Nonlinear Systems Subject to Measurement Delays

Sohaira Ahmad,Muhammad Rehan,Keum-Shik Hong,Raafia Majeed

doi:10.1155/2015/879492

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 againstL2norm-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.

Highlights

State estimation using an observer is a methodology widely employed in physical, biomedical, and engineering fields owing to its multitude of applications in road-gradient and vehicle-mass estimation, coestimation for lithium-polymer battery cells, online monitoring of nonlinear bioprocesses, identification and analysis of vascular tumor growth, detection and reconstruction of sensor faults, robust control of stochastic systems under disturbances, and cylinder-pressure reconstruction [1,2,3,4,5,6,7]
Two broad and widely employed methodologies for observer design of nonlinear systems are nonlinear state transformation, for which the state-estimation error dynamics are transformed into linear ones [19, 20], and the direct method, based on the original system, by which the estimation error dynamics are obtained in nonlinear form [21,22,23]
Motivated by the aforementioned linear delay-rangedependent approaches and one-sided Lipschitz nonlinear observer construction methodologies, the present study explores the problem of a nonlinear observer design for one-sided Lipschitz nonlinear systems under outputmeasurement and processing delays

Summary

Introduction

State estimation using an observer is a methodology widely employed in physical, biomedical, and engineering fields owing to its multitude of applications in road-gradient and vehicle-mass estimation, coestimation for lithium-polymer battery cells, online monitoring of nonlinear bioprocesses, identification and analysis of vascular tumor growth, detection and reconstruction of sensor faults, robust control of stochastic systems under disturbances, and cylinder-pressure reconstruction [1,2,3,4,5,6,7]. Observer synthesis for nonlinear systems has received considerable attention within the control field over the past few decades, as it makes possible the application of state estimation to control design, energy system analysis, fault diagnosis, chaos-based secure communications, synchronization studies, and unknown input recovery [8,9,10,11]. Notable work in this regard has been concentrated on continuous-time systems, while a certain quantity of research has been devoted to discrete-time and time-delay dynamical models [12,13,14,15]. These facts escalate the demand of the one-sided Lipschitz constant for approximating an upper bound on nonlinear component of a dynamical system to accomplish viable estimation of the full state vector

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