State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays

Abstract

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. The norm-bounded uncertainties enter into the system in a randomly way, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequence with known conditional probability. By constructing a new Lyapunov–Krasovskii functional, sufficient conditions are proposed to guarantee the convergence of the estimation error for all discrete time-varying delays, ROUs and distributed sensor delays. Subsequently, the explicit form of the estimator parameter is derived by solving two linear matrix inequalities (LMIs) which can be easily tested by using standard numerical software. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed estimation scheme.

Keywords:

• state estimation
• discrete nonlinear systems
• distributed sensor delays
• randomly occurring uncertainties.

Acknowledgments

The authors would like to thank the associate editor and anonymous reviewers for their valuable comments and suggestions that have helped improving the quality of this article.

Notes

This work was supported in part by the National Natural Science Foundation of China under [grant number 11301118], [grant number 11271103], the Science and Technology Foundation of Educational Commission of Heilongjiang Province under [grant number 12511608], and the Alexander von Humboldt Foundation of Germany.