Interval Observer Design Under Stealthy Attacks and Improved Event-Triggered Protocols

In this article, an interval estimation problem is investigated for a class of discrete-time nonlinear networked systems under stealthy attacks. An improved event-triggered protocol with the time-varying threshold is adopted to govern the received signals of interval observer so as to reduce unnecessary data communication burden. Stealthy attacks occurring in both the sensors and the plant come typically from open networked environments. For the addressed issue, a novel interval observer is developed to estimate the bounds of both system states and stealthy attacks. A sufficient condition is proposed by using the positive system theory and Lyapunov stability theory. Furthermore, the desired observer gain is obtained in terms of the solution to certain matrix inequalities. In comparison with the traditional approach that attacks are regarded as bounded disturbances, the estimated upper and lower bounds of attack signals can effectively reduce the conservatism of estimation performance, and avoid the implementation difficulties of the designed observer in practical engineering. Finally, the effectiveness of the proposed interval observers is verified by a numerical simulation.