# Non-Fragile Estimation for Nonlinear Delayed Complex Networks with Random Couplings Using Binary Encoding Schemes

## TL;DR

This paper proposes a non-fragile state estimator for complex networks with random delays and couplings, using binary encoding schemes to ensure reliable estimation despite transmission errors.

## Contribution

A novel non-fragile state estimation method is introduced for nonlinear complex networks with random couplings and time delays under binary encoding.

## Key findings

- A sufficient condition is derived for exponential ultimate boundedness of estimation errors under bit errors and random couplings.
- Simulation examples confirm the effectiveness of the proposed non-fragile estimator design.
- Estimator gains are obtained via optimization constrained by linear matrix inequalities.

## Abstract

This paper is dedicated to dealing with the design issue of a non-fragile state estimator for a type of nonlinear complex network subject to random couplings and random multiple time delays under binary encoding schemes (BESs). The BESs are put into use in the transmission of data from the sensor to the remote estimator. The phenomenon of bit errors is considered in the process of signal transmission, whose description utilizes a Bernoulli-distributed random sequence. The random couplings are represented by using the Kronecker delta function as well as a Markov chain. This paper aims to conduct a non-fragile state estimation such that, in the presence of some variations/perturbations in the gain parameter of the estimator, the estimation error dynamics will reach exponential ultimate boundedness in mean square and the ultimate bound will be minimized. Utilizing both stochastic analysis and matrix inequality processing, a sufficient condition is provided to guarantee that the constructed estimator satisfies the expected estimation performance, and the estimator gains are acquired by tackling an optimization issue constrained by some linear matrix inequalities. Eventually, two simulation examples are conducted, whose results verify that the approach to the design of a non-fragile estimator in this paper is effective.