A survey on interval observer design using positive system approach

Interval observers provide an interval state estimate for system states that cannot be measured directly at any moment. The core idea for the interval observer design is to provide the cooperativity of the estimated error dynamic system through a proper design. The interval observer can be implemented not only for general linear systems but also for complex nonlinear systems. This survey presents recent research on interval observer design methods for continuous-time systems, linear time-varying (LTV) discrete-time systems, bounded time-delay systems, nonlinear systems, and multi-agent systems (MASs) using the positive system approach. Moreover, it also introduces the practical applications of interval observer, such as fault detection in China Railway High-speed (CRH), security control of cyber–physical systems under cyber-attacks, and so on.