Ultimately Exponentially Bounded Estimates for a Class of Nonlinear Discrete-Time Stochastic Systems

In this paper, the ultimately exponentially bounded estimate problem of nonlinear stochastic discrete-time systems under generalized Lipschitz conditions is considered. A new sufficient condition making the estimation error system uniformly exponentially bounded in the mean square sense is given. The gain matrix can be obtained by solving matrix inequality. In the last section, numerical examples are provided verify the effectiveness of the conclusions.

Automated summary

This paper addresses the problem of ultimately exponentially bounded estimate for nonlinear stochastic discrete-time systems under generalized Lipschitz conditions. A new sufficient condition is proposed to ensure the uniform exponential boundedness of the estimation error system in the mean square sense. The gain matrix can be obtained by solving a matrix inequality. Numerical examples are provided in the last section to validate the effectiveness of the proposed conclusions.